Question 1

A researcher is comparing the average wind speed in Hopkins Forest during summer and winter. The mean wind speed in winter is 1.90 mph with a standard deviation of 1.29 mph, and in summer it is 1.11 mph with a standard deviation of 1.10 mph. If a day in winter has a wind speed of 4.0 mph and a day in summer has a wind speed of 3.0 mph, which day is more unusual relative to its season?

Accepted Answer

The winter day is more unusual because its z-score is higher.

Question 2

Which of the following best describes the effect of standardizing a data set using z-scores?

Accepted Answer

It shifts the mean to 0 and rescales the standard deviation to 1.

Question 3

A histogram of CEO compensation is highly skewed to the right. Which transformation would most likely make the distribution more symmetric?

Accepted Answer

Applying a logarithmic transformation to the data.

Question 4

Given a normal distribution with mean $$\mu = 100$$ and standard deviation $$\sigma = 15$$, what percentage of values fall between $$\mu - 2\sigma$$ and $$\mu + 2\sigma$$?

Accepted Answer

About 95%

Question 5

A student scores 720 on a test with a mean of 600 and a standard deviation of 60. What is the student's z-score?

Accepted Answer

$$z = \frac{720 - 600}{60} = 2.0$$

Question 6

Which of the following is NOT a requirement for a density curve?

Accepted Answer

The curve must be symmetric.

Question 7

A boxplot of cotinine levels shows a much larger spread for smokers compared to non-smokers. What does this indicate about the variability of cotinine levels?

Accepted Answer

Smokers have much greater variability in cotinine levels than non-smokers.

Question 8

If a distribution is unimodal and symmetric, which measure of center and spread are most appropriate to report?

Accepted Answer

Mean and standard deviation

Question 9

A timeplot of average wind speed over the year shows a clear seasonal trend. What is the main advantage of using a timeplot for this data?

Accepted Answer

It reveals patterns and trends over time that are not visible in other plots.

Question 10

Which of the following statements about outliers is TRUE?

Accepted Answer

Outliers can be important and may indicate exceptional cases.

Question 11

If you multiply every value in a data set by 2, what happens to the mean and standard deviation?

Accepted Answer

Both the mean and standard deviation are multiplied by 2.

Question 12

A normal probability plot of a data set is roughly a straight line. What does this indicate?

Accepted Answer

The data are approximately normally distributed.

Question 13

Which of the following is the correct formula for the z-score of a value $$x in a $$population with mean $$\mu$$ and standard deviation $$\sigma$$?

Accepted Answer

$$z = \frac{x - \mu}{\sigma}$$

Question 14

A histogram of income per world citizen is highly skewed to the right. What is a likely reason for this shape?

Accepted Answer

A small number of people have very high incomes, creating a long right tail.

Question 15

If a value has a z-score of -2.5, what does this mean?

Accepted Answer

The value is 2.5 standard deviations below the mean.

Question 16

Which of the following is a potential problem when comparing two histograms with different scales?

Accepted Answer

It can lead to misleading conclusions about the data.

Question 17

A researcher wants to know what proportion of a normal population falls between $$z = -1$$ and $$z = 1. $$What is the answer according to the 68-95-99.7 rule?

Accepted Answer

About 68%

Question 18

Which of the following is NOT a recommended step before applying the Normal model to a data set?

Accepted Answer

Assume the data are normal without checking the distribution.

Question 19

If the mean and standard deviation of a data set are both multiplied by 0.92, what transformation has occurred?

Accepted Answer

The data have been rescaled by multiplying each value by 0.92.

Question 20

Which of the following best describes the inflection point on a normal curve?

Accepted Answer

It is located exactly one standard deviation away from the mean.

Comparing and Summarizing Distributions & The Standard Deviation as a Ruler and the Normal Model

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