Week 9 — Midterm Exam (auto-graded) · Weeks 1–8

Course: Introduction to Statistics (18-week generic edition)
Coverage: Weeks 1–8 — Objectives 1–4 in full, plus Objective 5's normal-distribution portion.
Points: 100 (50 questions × 2 points) · Assignment group: Midterm (5% of grade) · Due: mid-week (the exam sits on day 4 of Week 9, after the review session) · Closed to AI.
Format: 43 multiple choice · 3 true/false · 3 multiple answer · 1 matching. Every item auto-graded. One attempt, time-bound. A calculator and — if your instructor permits — one page of notes are allowed; any z-table values an item needs are printed inside that item.

This is the human-readable exam with its vetted answer key and feedback. The import-ready Classic QTI is in L-midterm-week-09-qti.xml. The midterm is a low-stakes checkpoint (5%): it tells you how the first half consolidated, and it cannot sink a term of steady weekly work.

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Blueprint

The table below shows how the 50 items cover Weeks 1–8 — about six per week, plus two synthesis items that combine weeks.

Week	Items	Concepts tested
1	Q1–Q6, Q50	population vs. sample · parameter vs. statistic · NOIR levels · sampling methods (matching) · voluntary-response bias · observational vs. experiment · synthesis: statistic + self-selected sample
2	Q7–Q12	relative frequency · histogram reading · skew direction · truncated-axis trickery · choosing a display · outlier policy (T/F)
3	Q13–Q18	mean vs. median with an outlier · resistant center · computing s · 1.5×IQR fences · z-scores as standing · center-and-spread facts (multi)
4	Q19–Q24	explanatory vs. response · strength of r · r sees lines only · conditional percents · association via conditionals · lurking variables
5	Q25–Q30	long-run meaning of probability · complement · general addition rule · independent AND · conditional probability · gambler's fallacy (T/F)
6	Q31–Q36	discrete vs. continuous · legitimate distributions · E(X) · linear transformations · reading E(X) (multi) · shifts and spread (T/F)
7	Q37–Q42	the binomial setting · binomial formula · at least one · binomial mean & SD · cumulative technology · B·I·N·S conditions (multi)
8	Q43–Q49	empirical rule · z-scores · forward normal · inverse normal · comparing z-scores · assessing normality · synthesis: binomial mean/SD + the 95% band

Distractors target the misconceptions named in the Weeks 1–8 outlines (numbers that label, skew named for the peak, variance-for-SD, wrong denominator, adding non-disjoint probabilities, value-averaging E(X), the forgotten ways factor, the wrong tail). No trick questions; no item depends on remembering any specific dataset.

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Questions, key, and feedback

Q1 (MC). A 250-room hotel wants the average check-in time for all 38,000 guest stays it hosted over the past year. Its front-desk system pulls a random 600 of those stays and computes their average check-in time. The sample is —
- A. All 38,000 guest stays from the past year
- B. The 600 randomly pulled guest stays ✅
- C. The average check-in time of the 600 stays
- D. The hotel's 250 rooms
Feedback: The sample is the part actually measured — the 600 pulled stays. All 38,000 stays are the population; the 600 stays' average is a statistic.

Q2 (MC). In a random sample of 90 cartons sold at a farm stand, 18 contained at least one cracked egg, so the owner reports the sample proportion p̂ = 0.20. The corresponding parameter is —
- A. The value 0.20 computed from the sampled cartons
- B. The 90 cartons that were selected and inspected
- C. The proportion with a cracked egg among all cartons the stand sells ✅
- D. The 18 sampled cartons that contained a cracked egg
Feedback: 18 ÷ 90 = 0.20 is the statistic (from the sample); the matching parameter is the true proportion across all cartons — the value we never see directly.

Q3 (MC). A dog park's sign-in sheet records, for each visit: the dog's registration tag number, the owner's satisfaction rating (poor / fair / good / excellent), and the visit length in minutes. In that order, the levels of measurement are —
- A. Nominal, ordinal, and ratio ✅
- B. Ratio, interval, and nominal
- C. Nominal, interval, and interval
- D. Ordinal, ordinal, and ratio
Feedback: A tag number labels (nominal); the rating is ordered with unmeasurable gaps (ordinal); minutes have a true zero (ratio).

Q4 (Matching). A park system wants opinions from its 12,000 camping-permit holders. Match each plan to the sampling method it uses.

Prompt	Correct match
Number all 12,000 permit holders and randomly draw 300 of them	Simple random sample
Split holders into tent, RV, and cabin campers; randomly sample within each group	Stratified sample
Randomly choose 3 of the system's 15 campgrounds and survey every camper staying there	Cluster sample
From an alphabetical list, take every 40th permit holder after a random start	Systematic sample
Feedback: Stratified samples within every group; cluster takes whole groups; systematic walks the list; the SRS is names in a hat.

Q5 (MC). A car wash posts a web poll on its homepage: "Tap here to rate your last wash!" Among customers who choose to respond, 78% report a problem. The most serious flaw in this poll is —
- A. Undercoverage, because the poll cannot reach people who never wash a car
- B. A census error, because the poll reached every customer of the car wash
- C. Cluster sampling, because respondents arrive naturally in groups
- D. Voluntary response bias — the customers who opt in tend to have strong feelings ✅
Feedback: Opt-in polls over-collect the delighted and the furious; the indifferent middle stays silent. More replies would just be more of the same lean.

Q6 (MC). A plant nursery notices that customers who attend its free weekend workshops spend more per visit than customers who do not. No one was assigned to attend. Which statement is justified?
- A. The workshops cause higher spending, since the gap between groups is large
- B. This counts as an experiment, because two groups of customers were compared
- C. Attending workshops must lower spending once other variables are considered
- D. This is observational — existing gardening enthusiasm could drive both attendance and spending ✅
Feedback: Nothing was imposed, so this is observational: a link, not an arrow. A confounder (enthusiasm) plausibly drives both.

Q7 (MC). A movie theater tallies the snack chosen by 60 concession customers: popcorn 27, candy 15, nachos 12, pretzels 6. The relative frequency of candy is —
- A. 0.15
- B. 0.25 ✅
- C. 0.45
- D. 15
Feedback: Relative frequency = count ÷ total = 15 ÷ 60 = 0.25. (0.45 is popcorn's share; 15 is the raw count.)

Q8 (MC). A histogram of 50 recorded escape-room finish times has these classes (minutes) and counts — 30–<40: 8; 40–<50: 17; 50–<60: 15; 60–<70: 10. How many of the 50 teams finished in under 50 minutes?
- A. 25 teams ✅
- B. 8 teams
- C. 17 teams
- D. 40 teams
Feedback: Add the classes below 50: 8 + 17 = 25 teams.

Q9 (MC). In one bowling league, most members' season-average scores cluster between 170 and 200, while a few members average far lower, down near 120. The distribution of season averages is —
- A. Skewed to the right, because the tall peak sits at the high scores
- B. Symmetric, because most of the scores land close to one another
- C. Skewed to the left, because the thin tail stretches toward the low scores ✅
- D. Uniform, because scores are free to land anywhere from 120 to 200
Feedback: Skew is named for the tail, not the peak — the tail tells the tale, and here it stretches left toward 120.

Q10 (MC). An arcade's poster compares tokens redeemed at its two locations with a bar chart: East 5,200 tokens, West 5,000 — but the vertical axis starts at 4,900. What makes the poster misleading?
- A. Bar charts can never be used for token counts, which are quantitative
- B. The truncated axis makes a 4% difference look several times larger than it is ✅
- C. Nothing — the 200-token gap is real, so the picture is honest
- D. Token counts are parts of one whole, so a pie chart was required instead
Feedback: With the axis starting at 4,900, the bars stand 300 vs. 100 tall — a 4% gap drawn as a 3-to-1 ratio. Bars start at zero.

Q11 (MC). A park office wants to display the shape of the 180 nightly stay lengths (in nights) recorded at one campground this season. The best display is —
- A. A pie chart with one slice for each different stay length
- B. A bar chart with its bars sorted from tallest to shortest
- C. Any of these displays works equally well for stay lengths
- D. A histogram, since stay length is a quantitative variable ✅
Feedback: Shape lives on a number line: quantitative data → histogram (touching bars, fixed order). Separated, sortable bars are for categories.

Q12 (True / False). True or False: A value that sits far from the rest of the data should be investigated as a possible error or a real extreme — never silently deleted.
- True ✅
- False
Feedback: True. Outliers are flags, not garbage: fix errors, report real extremes, and let a formal rule (like 1.5×IQR) do the flagging.

Q13 (MC). Five bowlers' scores in one league night were 152, 154, 156, 158, and 190. Which statement is correct?
- A. The mean is 162 and the median is 156 ✅
- B. The mean is 156 and the median is 162
- C. The mean is 162 and the median is 155
- D. The mean and the median both equal 162
Feedback: Sum 810 ÷ 5 = 162 (the 190 pulls the mean up); the sorted middle value is 156. The mean chases the tail; the median doesn't.

Q14 (MC). Nightly rates for the 400 bookings at a beach hotel last month are strongly right-skewed by a handful of luxury-suite bookings. To report a typical nightly rate, the hotel should use —
- A. The median, because it resists the pull of the few luxury-suite rates ✅
- B. The mean, because it uses the exact value of every booking's rate
- C. The range, because it spans the cheapest through priciest bookings
- D. The mode, because the most frequent rate is by definition typical
Feedback: Skewed data report the median — the mean chases the luxury-suite tail upward.

Q15 (MC). A farm stand weighs five eggs from one hen: 53, 59, 60, 61, and 67 grams, with mean 60 grams. The sample standard deviation is —
- A. 25 grams
- B. 14 grams
- C. 5 grams ✅
- D. 20 grams
Feedback: Deviations −7, −1, 0, 1, 7 → squares sum to 100 → 100 ÷ 4 = 25 → √25 = 5 grams. (25 is the variance; 14 is the range.)

Q16 (MC). Thirty escape-room attempts have the five-number summary min = 31, Q1 = 40, median = 47, Q3 = 54, max = 79 (minutes). Using the 1.5×IQR rule, the upper fence is —
- A. 68 minutes, so the 79-minute attempt is flagged as an outlier
- B. 75 minutes, so the 79-minute attempt is flagged as an outlier ✅
- C. 54 minutes, the value of the third quartile itself
- D. 96 minutes, so no attempt at all is flagged as an outlier
Feedback: IQR = 54 − 40 = 14; upper fence = 54 + 1.5(14) = 75; the 79-minute attempt lies beyond it. (68 adds only one IQR.)

Q17 (MC). A camper's tent went up in 12 minutes at a park where setup times average 18 minutes with a standard deviation of 4 minutes. The z-score for this setup is —
- A. −6, because the setup beat the average by six full minutes
- B. −0.375, dividing the difference by the variance of 16
- C. +1.5, because a fast setup counts as above average
- D. −1.5, meaning 1.5 standard deviations below the mean time ✅
Feedback: z = (12 − 18) ÷ 4 = −1.5. The sign is direction (below the mean), not a judgment — for a time, below average is fast.

Q18 (Multiple answer — select all that apply). A study group is quizzing each other on measures of center and spread. Select every claim below that is correct.
- A. A sample standard deviation can be negative when most values sit below the mean
- B. For an even count of values, the median is the average of the two middle values ✅
- C. The IQR measures the width of the middle 50% of the data ✅
- D. The range is resistant to extreme values
- E. The variance equals the square of the standard deviation, in squared units ✅
Feedback: s is never negative, and the range is owned by the two end values — the least resistant summary there is.

Q19 (MC). A plant nursery will use the weekly fertilizer amount (grams) given to a seedling to predict the seedling's height (cm) at eight weeks. The explanatory variable is —
- A. Seedling height, plotted on the x-axis
- B. Fertilizer amount, plotted on the y-axis
- C. Fertilizer amount, plotted on the x-axis ✅
- D. Seedling height, because it is measured last
Feedback: The predictor (explanatory) goes on x; the outcome (response — height) goes on y.

Q20 (MC). At a dog park, the correlation between dogs' ages and their visit lengths is r = −0.78; the correlation between dogs' weights and their visit lengths is r = +0.42. Which comparison is correct?
- A. The age relationship is stronger, because 0.78 sits farther from zero than 0.42 ✅
- B. The weight relationship is stronger, because a positive r always beats a negative one
- C. The two relationships are equally strong, since both values stay below 1
- D. The age relationship is weaker, because a negative r signals a fading link
Feedback: Strength is distance from 0; the sign only gives the direction. |−0.78| > |+0.42|.

Q21 (MC). A car wash records the daily temperature and the number of cars washed for 40 days. The scatterplot shows a clear arch — washes rise with temperature, peak in the 70s, then fall in extreme heat — and r = 0.05. The best conclusion is —
- A. Temperature and wash counts are unrelated, since r is nearly zero
- B. A strong relationship exists, but a curved one that r cannot measure ✅
- C. Each extra degree of temperature brings about 5% more washes
- D. The data must contain an entry error, because patterns require large r
Feedback: r sees straight lines only. A strong arch can produce r ≈ 0 — always look at the plot before trusting the number.

Q22 (MC). A 240-stay sample at a resort hotel: of 150 weekday stays, 45 used the pool; of 90 weekend stays, 63 used the pool. What percent of weekend stays used the pool?
- A. 26%, dividing the 63 weekend pool users by all 240 stays
- B. 70%, dividing the 63 weekend pool users by the 90 weekend stays ✅
- C. 45%, because 108 of the 240 stays overall used the pool
- D. 58%, dividing the 63 weekend pool users by all 108 pool users
Feedback: "Among weekend stays" makes 90 the denominator: 63 ÷ 90 = 70%. The denominator is the whole game.

Q23 (MC). Using that same 240-stay sample (weekday: 45 of 150 used the pool; weekend: 63 of 90), which comparison settles whether pool use is associated with day type?
- A. Comparing the 150 weekday stays with the 90 weekend stays
- B. Comparing the largest single cell count with the table's grand total
- C. Checking whether all four cell counts in the table are exactly equal
- D. Comparing 30% pool use among weekday stays with 70% among weekend stays ✅
Feedback: Association means the conditional distributions differ across groups: 45/150 = 30% vs. 63/90 = 70%.

Q24 (MC). Across many weekends, a town's dog-park visit counts and its car-wash revenues rise and fall together. The most reasonable explanation is —
- A. Trips to the dog park cause people to wash their cars afterward
- B. Car washing causes dog-park visits, since errands cluster together
- C. A lurking variable — good weather — plausibly drives both activities ✅
- D. The association is proof of coincidence and would vanish with more data
Feedback: Sunny weekends send dogs to the park and cars to the wash. Hunt the third variable before accepting any arrow.

Q25 (MC). A park's records show that the probability a walk-up camper gets a same-day campsite is 0.15. Which statement best interprets this number?
- A. Over many walk-ups, about 15% end up getting a same-day campsite ✅
- B. Exactly 3 of every 20 walk-up campers will get a same-day campsite
- C. If 100 campers walk up, exactly 15 of them will get a campsite
- D. After one camper gets a site, the next several walk-ups must be turned away
Feedback: Probability is a long-run promise, not a short-run guarantee — no exact count in any finite batch is assured.

Q26 (MC). A car wash's sensor logs show that the probability a vehicle needs a second rinse cycle is 0.07. The probability that a vehicle does NOT need a second rinse is —
- A. 0.07
- B. 0.14
- C. 1.07
- D. 0.93 ✅
Feedback: P(not A) = 1 − P(A) = 1 − 0.07 = 0.93. (1.07 is past the 0-to-1 scale — the built-in smoke alarm.)

Q27 (MC). At a farm stand, 40% of customers buy eggs, 25% buy honey, and 10% buy both. The probability that a randomly chosen customer buys eggs or honey (or both) is —
- A. 0.10
- B. 0.55 ✅
- C. 0.65
- D. 0.75
Feedback: P(A or B) = 0.40 + 0.25 − 0.10 = 0.55 — subtract the overlap so the both-buyers aren't counted twice.

Q28 (MC). An arcade game pays out a bonus token on 30% of plays, independently from play to play. The probability that two plays in a row both pay a bonus token is —
- A. 0.09 ✅
- B. 0.15
- C. 0.30
- D. 0.60
Feedback: Independent AND multiplies: 0.30 × 0.30 = 0.09. (0.60 adds — that's the OR move, and the wrong one here.)

Q29 (MC). One day's dog-park log lists 80 dogs: 50 large dogs, of which 10 visited the agility area, and 30 small dogs, of which 12 visited the agility area. P(visited the agility area | small dog) is —
- A. 0.15
- B. 0.275
- C. 0.40 ✅
- D. 0.55
Feedback: Given "small dog," the world shrinks to 30 dogs: 12 ÷ 30 = 0.40. (12 ÷ 80 = 0.15 ignores the given; 12 ÷ 22 answers the flipped question.)

Q30 (True / False). True or False: An arcade game that has not paid a bonus token in 15 straight plays becomes more likely to pay one on the next play, because results even out.
- True
- False ✅
Feedback: False — independent plays have no memory. The long run fixes proportions by swamping, never by compensating.

Q31 (MC). A car wash logs several quantities all day. Which one is a discrete random variable?
- A. The exact time a car spends inside the wash tunnel
- B. The exact volume of soap dispensed during one wash
- C. The number of cars waiting in the queue at noon ✅
- D. The exact temperature of the rinse water in one cycle
Feedback: Discrete you count, continuous you measure — a queue length is a countable 0, 1, 2, …

Q32 (MC). Let X = the number of drinks in a randomly chosen concession order, with P(0) = 0.20, P(1) = 0.45, P(3) = 0.10 — and the entry for P(X = 2) smudged out. P(X = 2) must be —
- A. 0.15
- B. 0.35
- C. 0.75
- D. 0.25 ✅
Feedback: Probabilities must total 1: 1 − (0.20 + 0.45 + 0.10) = 0.25. (0.75 forgets the final subtraction's other entries.)

Q33 (MC). A token vending machine at an arcade occasionally dispenses extra tokens. Let X = the number of extra tokens with one purchase: P(0) = 0.40, P(1) = 0.35, P(2) = 0.20, P(4) = 0.05. E(X) is —
- A. 0.75
- B. 0.95 ✅
- C. 1.00
- D. 1.75
Feedback: E(X) = 0(0.40) + 1(0.35) + 2(0.20) + 4(0.05) = 0.95 extra tokens per purchase, long-run. (1.75 averages the values and ignores the probabilities.)

Q34 (MC). An escape room's hint count per team, X, has mean 1.5 and SD 0.5. The room charges a flat $60 booking fee plus $10 per hint, so a team's cost is Y = 60 + 10X. The mean and SD of Y are —
- A. Mean $75 and SD $5 ✅
- B. Mean $75 and SD $65
- C. Mean $15 and SD $5
- D. Mean $75 and SD $0.50
Feedback: E(Y) = 60 + 10(1.5) = 75; SD(Y) = 10 × 0.5 = 5. Adding shifts the center only; multiplying rescales the spread.

Q35 (Multiple answer — select all that apply). A hotel's records give X = the number of room-service orders per stay, with a legitimate probability distribution and E(X) = 0.6. Which statements are correct? Select all that apply.
- A. Exactly 60% of stays place one room-service order
- B. Over many stays, room-service orders average about 0.6 per stay ✅
- C. The probabilities in X's distribution sum to exactly 1 ✅
- D. The most likely value of X must be 0.6
- E. E(X) can be a value that no single stay ever equals ✅
Feedback: Expected value is what you'd average, not what you'd expect — 0.6 orders never happens on one stay, and that's fine.

Q36 (True / False). True or False: If a campground adds a flat $3 fee to every nightly bill, the standard deviation of the nightly bills increases by $3.
- True
- False ✅
Feedback: False — a shift slides every bill together and leaves the spacing (SD) unchanged. Only multiplying rescales spread.

Q37 (MC). A 40-room inn takes 10 reservations for one night; each reservation independently no-shows with probability 0.1. Which variable below is binomial?
- A. The number of reservations taken until the first no-show occurs
- B. The arrival time, in minutes after check-in opens, of the earliest guest
- C. The number of no-shows next month, however many reservations occur
- D. The number of the 10 booked reservations that no-show that night ✅
Feedback: B·I·N·S: binary outcome, independent trials, n = 10 fixed in advance, same p = 0.1. "Until the first…" has no fixed n.

Q38 (MC). At a dog-park agility demo, each of 4 dogs clears the high jump independently with probability 0.5. The probability that exactly 2 of the 4 clear it is —
- A. 0.375 ✅
- B. 0.0625
- C. 0.25
- D. 0.75
Feedback: C(4, 2) × 0.5² × 0.5² = 6 × 0.0625 = 0.375 — ways × wins × losses. Forgetting the 6 ways gives 0.0625.

Q39 (MC). Each carton packed at a farm stand independently contains a double-yolk egg with probability 0.2. If a customer buys 3 cartons, the probability that at least one contains a double-yolk egg is —
- A. 0.008
- B. 0.200
- C. 0.488 ✅
- D. 0.600
Feedback: P(at least one) = 1 − P(none) = 1 − 0.8³ = 1 − 0.512 = 0.488. (0.600 adds 0.2 three times — probabilities of non-disjoint events don't add.)

Q40 (MC). A theater's app shows that 25% of ticket buyers redeem a concession coupon, independently. For 300 ticket buyers, the mean and standard deviation of the number who redeem are —
- A. Mean 75 and SD 56.25
- B. Mean 75 and SD 7.5 ✅
- C. Mean 75 and SD 8.66
- D. Mean 150 and SD 7.5
Feedback: μ = np = 300(0.25) = 75; σ = √(300 × 0.25 × 0.75) = √56.25 = 7.5. (56.25 is the variance still waiting for its square root.)

Q41 (MC). A manager wants the chance of seeing 5 or fewer coupon redemptions among 20 customers when each redeems independently with probability 0.3. Which spreadsheet entry computes it?
- A. =BINOM.DIST(5, 20, 0.3, FALSE)
- B. =BINOM.DIST(20, 5, 0.3, TRUE)
- C. =BINOM.DIST(5, 20, 0.3, TRUE) ✅
- D. =BINOM.DIST(0.3, 20, 5, TRUE)
Feedback: "5 or fewer" is cumulative — argument order k, n, p, and TRUE for P(X ≤ k). FALSE would give exactly 5 only.

Q42 (Multiple answer — select all that apply). A ranger checks 15 randomly chosen campsites each evening; each site independently has a rule violation with probability 0.1. For X = the number of sites with a violation to be binomial, which conditions must hold? Select all that apply.
- A. The number of sites checked is fixed before the checks begin ✅
- B. The violation probability must equal exactly 0.5
- C. Each site's violation status is independent of the other sites ✅
- D. The number of violations must be known before checking starts
- E. The probability of a violation is the same at every site ✅
Feedback: B·I·N·S needs a fixed n, independence, and the same p — any p between 0 and 1 qualifies, and the count is never known in advance.

Q43 (MC). Completion times for one escape room are approximately normal with mean 48 minutes and SD 6 minutes. About 95% of completion times fall between —
- A. 42 and 54 minutes
- B. 30 and 66 minutes
- C. 24 and 72 minutes
- D. 36 and 60 minutes ✅
Feedback: 95% lives within 2 SDs: 48 ± 12 → 36 to 60 minutes. (42–54 is the 68% band; 30–66 is the 99.7% band.)

Q44 (MC). Egg weights at a farm stand are approximately normal with mean 58 grams and SD 4 grams. One egg weighs 53 grams. Its z-score is —
- A. +1.25, meaning 1.25 standard deviations above the mean
- B. −1.25, meaning 1.25 standard deviations below the mean ✅
- C. −5, meaning five standard deviations below the mean
- D. −0.3125, dividing the difference by the variance of 16
Feedback: z = (53 − 58) ÷ 4 = −1.25 — divide by the SD, never the variance, and read the sign as direction.

Q45 (MC). A car wash's full-service times are approximately normal with mean 30 minutes and SD 4 minutes. Using the course z-table (the area to the left of z = 1.25 is 0.8944), the proportion of services finishing in under 35 minutes is —
- A. 0.8944 ✅
- B. 0.1056
- C. 0.9332
- D. 1.25
Feedback: z = (35 − 30) ÷ 4 = 1.25 → left-tail area 0.8944. (0.1056 is the other tail; 1.25 is a z, not a proportion.)

Q46 (MC). Hotel housekeeping times are approximately normal with mean 24 minutes and SD 4 minutes. Management wants a target time that only about 6.68% of rooms exceed. Using the course z-table (the area to the left of z = 1.5 is 0.9332), the target should be —
- A. 30 minutes — 1.5 standard deviations above the mean ✅
- B. 18 minutes — 1.5 standard deviations below the mean
- C. 28 minutes — exactly one standard deviation above the mean
- D. 36 minutes — three standard deviations above the mean
Feedback: "Only 6.68% exceed" means 93.32% fall below → z = 1.5 → 24 + 1.5(4) = 30 minutes. A cutoff above the mean adds z·σ.

Q47 (MC). Priya bowls in a league whose scores are approximately N(140, 20); her score this week is 180. Dev bowls in a league with scores approximately N(190, 10); his score is 205. Who performed better relative to their own league?
- A. Dev, because his 205 is the higher raw score
- B. Dev, because his league's smaller SD makes every score steadier
- C. Neither, because scores from different leagues can never be compared
- D. Priya, because her z-score of 2.0 beats Dev's z-score of 1.5 ✅
Feedback: Priya: (180 − 140)/20 = 2.0; Dev: (205 − 190)/10 = 1.5. z-scores put different scales on one ruler — that's their whole job.

Q48 (MC). A campground's 150 nightly noise-complaint counts are strongly right-skewed, with many zeros and a few large values. A staffer proposes using a normal model with the counts' mean and SD to publish percentage claims. The best response is —
- A. The model applies, because 150 nights is a large enough sample
- B. The normal model fits poorly here, so its percentage claims would be unreliable ✅
- C. The model applies automatically, because the counts are numeric
- D. The empirical rule still guarantees 95% of counts lie within 2 SDs
Feedback: The empirical rule's password is IF bell-shaped — a strongly skewed pile of counts fails the audition, whatever its size.

Q49 (MC). A player makes 400 independent plays of an arcade game; each play wins a token with probability 0.5. Using μ = np and σ = √(np(1−p)) — and the fact that this count's histogram is approximately bell-shaped for so many plays — about 95% of such 400-play sessions win between —
- A. 190 and 210 tokens
- B. 170 and 230 tokens
- C. 180 and 220 tokens ✅
- D. 100 and 300 tokens
Feedback: μ = 400(0.5) = 200; σ = √(400 × 0.5 × 0.5) = √100 = 10; the 95% band is μ ± 2σ = 180 to 220 — Week 7's engine driving Week 8's rule.

Q50 (MC). A hotel emails a comment-card link to all 6,200 guests who stayed last month; 380 reply, and 62% of the replies rate breakfast "excellent." The manager wants the percent of ALL last-month guests who would say excellent. Which statement is correct?
- A. The 62% is the parameter, because it describes every guest who replied
- B. With 380 replies, the sample is large enough to remove selection bias
- C. The 62% must be trustworthy, because every guest received the email
- D. The 62% is a statistic from a voluntary-response sample, so it may be biased ✅
Feedback: Only repliers were measured — an opt-in sample. The 62% is a statistic, and no reply count repairs a self-selected method.

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Answer key (quick reference)

The table lists each item's keyed answer; the matching item shows its four pairs abbreviated.

Q	Answer	Q	Answer
1	B	26	D
2	C	27	B
3	A	28	A
4	Number all 12,000 permit h…→ Simple random sample / Split holders into tent, R…→ Stratified sample / Randomly choose 3 of the s…→ Cluster sample / From an alphabetical list,…→ Systematic sample	29	C
5	D	30	False
6	D	31	C
7	B	32	D
8	A	33	B
9	C	34	A
10	B	35	B, C, E
11	D	36	False
12	True	37	D
13	A	38	A
14	A	39	C
15	C	40	B
16	B	41	C
17	D	42	A, C, E
18	B, C, E	43	D
19	C	44	B
20	A	45	A
21	B	46	A
22	B	47	D
23	D	48	B
24	C	49	C
25	A	50	D

Quality gate (self-checked, exam-week findings gates): every single-answer item has exactly one correct option by construction, and every computed value (means, SDs, fences, probabilities, E(X), binomial and normal results) is re-verified in the Week 9 math script. (a) Key sequence: the 43 MC keys run B C A D D B A C B D A A C B D C A B B D C A D B A C C D B A D A C B C D B A A D B C D — letters land 11/11/10/11 with no letter above 26%, no run longer than 2, no ABCD cycling, and a cyclic-successor rate of about 21% (chance-like); no stem references an option letter, so re-permutation stays safe. (b) Option length: the keyed option is the strictly longest in 10 of 43 MC items and strictly shortest in 3 of 43 (both far under the 50% ceiling), and every item's key/distractor mean-length ratio sits inside 0.5–1.5. (c) Zero leakage: an automated token-overlap screen compared all 50 stems against all 25 practice-exam stems (threshold 0.45) and against every weekly quiz item in the pack (threshold 0.50) — no pair crosses either line, and no recall-style "name the whole list" stems appear. (d) Consistency: the study guide (M) was cross-checked section-by-section against the Weeks 1–8 chapters' Key terms and Summaries, so nothing this exam grades contradicts what the course taught. Fresh scenario surfaces throughout (hotel check-ins, movie-theater concessions, plant nursery, arcade tokens, camping permits, dog-park visits, bowling-league scores, escape-room times, farm-stand eggs, car-wash queues) — none reuse a quiz, practice-set, lab, chapter self-check, or assignment surface from Weeks 1–8.

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Item-bank note

All 50 items are tagged by week and concept (idents mtq1–mtq50) and deposited in Item Bank: Midterm — Weeks 1–8. They are fresh variants of the weekly banks' tested concepts — never the weekly quizzes' live stems — and the practice exam (pmq1–pmq25) shares zero items with this exam. Per-term variant updates regenerate from the same concept map.

Canvas placement block

canvas_object    = Quizzes::Quiz
title            = "Midterm Exam — Weeks 1–8"
assignment_group = "Midterm"
points_possible  = 100
grading_type     = points
due_offset_days  = 4        # the exam sits mid-week: review first, debrief after
published        = true
shuffle_answers  = true
one_question_at_a_time = recommended
notes            = "Closed to AI. Calculator allowed; one page of notes if the instructor permits. Needed z-table values are printed inside the items that use them."