Week 9 Quiz

In a normal model, about what percent of values lie within two standard deviations of the mean?

Select one.

• About 68%
• About 95%
• About 99.7%
• About 50%

Suppose one-way commute times follow a normal model with mean μ = 32 minutes and standard deviation σ = 6 minutes. Between what two commute times do about 68% of trips fall?

Select one.

• Between 20 and 44 minutes
• Between 29 and 35 minutes
• Between 26 and 38 minutes
• Between 14 and 50 minutes

Suppose one-way commute times follow a normal model with mean μ = 32 minutes and standard deviation σ = 6 minutes. What is the z-score for a commute of 38 minutes? Enter a whole number only.

Type a short answer.

Suppose one-way commute times follow a normal model with mean μ = 32 minutes and standard deviation σ = 6 minutes. The standard normal table gives 0.8413 as the area to the left of z = 1. What proportion of trips take longer than 38 minutes?

Select one.

• 0.1587
• 0.8413
• 0.6827
• 0.3174

Suppose one-way commute times follow a normal model with mean μ = 32 minutes and standard deviation σ = 6 minutes. The z-score with 95% of the area to its left is 1.645. What commute time is the 95th percentile?

Select one.

• 22.13 minutes
• 38.00 minutes
• 43.76 minutes
• 41.87 minutes

A transit planner wants the range that holds the middle 95% of a normal model of trip times. Which z-scores mark the two ends of that range?

Select one.

• z = ±1.645
• z = ±1.960
• z = ±2.576
• z = ±1.000

All 342 measured penguin body masses lie within three standard deviations of their mean. True or false: this one check shows that the body masses are normally distributed.

True or false.

• True
• False

The 342 measured penguin body masses have a mean of 4,201.75 g and a median of 4,050 g. The median sits 500 g above the first quartile but 700 g below the third quartile. Which verdict fits these checks?

Select one.

• A normal model is reasonable, because no body mass is flagged as an outlier
• A normal model is reasonable, because the mean and the median are both near 4,000 g
• A normal model is not reasonable for fine tail questions, because the masses lean right
• A normal model is not reasonable, because the masses lean left toward the lighter birds

Which of these are checks you can run to judge whether a normal model is reasonable for a set of data? Select all that apply.

Select every option that applies.

• Look at whether the histogram is single-peaked and roughly symmetric
• Compare the mean with the median
• Read whether a normal probability plot falls close to a straight line
• Look up the area to the left of z = 1 in a standard normal table
• Count whether the data set holds at least 30 values

For which of these data sets would the empirical rule (68%, 95%, 99.7%) be least appropriate?

Select one.

• Home sale prices in a town where a few mansions sold for far more than the rest
• Fill weights of rice bags from one machine, piled symmetrically around the label weight
• Heights of adult sunflowers in one garden, single-peaked and roughly symmetric
• Counts of right answers when guessing on 100 four-option questions