AP Stats Mid Year

A group of students played a game in which they earned points for answering questions correctly. The following dotplot shows the total number of points earned by each student. Which of the following is the best description of the distribution of points earned?

• Approximately normal

• Bimodal without a gap

• Bimodal with a gap

• Skewed to the right without a gap

• Skewed to the right with a gap

Janelle collected data on the amount of time in minutes each person in a large sample of customers spent in a local store. The data also included recording the gender of each customer. These data were used to generate the boxplots shown below. Which of the following statements is true?

• The range in the amount of time in minutes males in the sample of customers spent in the store is approximately 40 minutes.

• The mean amount of time in minutes males in the sample of customers spent in the store is approximately 20 minutes.

• The third quartile of the amount of time in minutes males in the sample of customers spent in the store is approximately 45 minutes.

• The interquartile range of the amount of time in minutes females in the sample of customers spent in the store is 15 minutes.

• Approximately half of the males in the sample of customers spent at least as much time in the store as any female in the sample of customers.

The figure above summarizes the heights, in centimeters, of approximately 400 pine seedlings six years after they were planted at a center for environmental study. Approximately half of the trees were fertilized yearly, and the remaining trees were never fertilized. Which of the following statements about the medians and interquartile ranges (IQRs) of the heights of the two groups of trees 6 years after being planted is true?

• The medians and IQRs are the same for the unfertilized trees and the fertilized trees.

• The median for the unfertilized trees is greater than the median for the fertilized trees, and the IQR is also greater for the unfertilized trees.

• The median for the unfertilized trees is the same as the median for the fertilized trees, and the IQR is greater for the unfertilized trees.

• The median for the unfertilized trees is less than the median for the fertilized trees, and the IQR is greater for the unfertilized trees.

• The median for the unfertilized trees is less than the median for the fertilized trees, and the IQR is less for the unfertilized trees.

Researchers are investigating how the amount of monthly rainfall, measured in centimeters (cm), affects the monthly growth, in cm, of a certain plant. From a sample of data, the researchers created a least-squares regression line. Computer output is shown in the following table. Which of the following statements is an interpretation of the value 0.75 shown in the table?

• Monthly growth is expected to increase by 0.75 cm when rainfall increases by 1 cm.

• Rainfall is expected to increase by 0.75 cm when monthly growth increases by 1 cm.

• For a month with 0 cm of rainfall, the monthly growth is expected to be approximately 0.75 cm.

• For a plant with 0 cm of monthly growth, the month had an expected rainfall of approximately 0.75 cm.

• Approximately 75% of the variability in monthly growth is due to its linear relationship with rainfall.

• A

• B

• C

• D

• E

Is this a probability distribution?

• No, the sum of p(x) does not equal 1.

• Yes, all p(x) are between 0 and 1.

• No, all p(x) are not between 0 and 1.

• Yes, the sum p(x) is 1.

Is this a probability distribution?

• No

• Yes

A common measure of flexibility is the sit-and-reach test, where a person sits on the floor with legs straight in front. The person then reaches as far forward as possible, and the distance reached past the feet is recorded. The histograms summarize the results of the sit-and-reach test for two groups, young adult men and middle-aged men. Negative distances represent a reach that is not as far as the feet. Which of the following statements is the best description of the distributions of distances?

• The distribution for young adult men is approximately symmetric, and the distribution for middle-aged men is skewed to the right.

• The distribution for young adult men is approximately symmetric, and the distribution for middle-aged men is skewed to the left.

• The distribution for young adult men is skewed to the right, and the distribution for middle-aged men is approximately symmetric.

• The distribution for young adult men is skewed to the left, and the distribution for middle-aged men is approximately symmetric.

• The distribution for young adult men is skewed to the left, and the distribution for middle-aged men is skewed to the right.

A random sample of middle school students from District 1 and a random sample of middle school students from District 2 were selected with an even number of students in each sample. The number of minutes each student spent playing a certain mobile game application in a typical day was recorded. The data are summarized in the following table. If no two students within each district spent the same amount of time playing the mobile game application, which statement must be true?

• The number of students in the sample from District 1 was less than the number of students in the sample from District 2.

• The percentage of students in both samples who spent less than 130 minutes playing the game is equal.

• No students in either district spent 115 minutes playing the game.

• The range of the number of minutes spent playing the game was greater for the District 1 sample than for the District 2 sample.

• The interquartile range of the number of minutes spent playing the game was less for the District 1 sample than for the District 2 sample.

Heights, in inches, for the 200 graduating seniors from Washington High School are summarized in the frequency table below. Which of the following statements about the median height is true?

• It is greater than or equal to 78 inches.

• It is greater than or equal to 72 inches but less than 78 inches.

• It is greater than or equal to 66 inches but less than 72 inches.

• It is greater than or equal to 60 inches but less than 66 inches.

• It is less than 60 inches.