AP Stat Chapter 2

In 1965, the mean price of a new car was $2,650 and the standard deviation was $1,000. In 2011, the mean was $30,500 and the standard deviation was $9,000. If a Ford Mustang cost $2,300 in 1965 and $28,000 in 2011, in which year was it more expensive relative to other cars?

• 1965, because the standardized score is greater than in 2011.

• 1965, because the standard deviation is smaller.

• 2011, because the standardized score is greater than in 1965.

• 2011, because $28,000 is greater than $2,300.

• We cannot compare the two prices, because we don’t know if the prices for each year are Normally distributed.

. The weights of adult male Labrador Retrievers are approximately Normally distributed with a mean of 87 pounds and a standard deviation of 8 pounds. Which of the following statements is true?

• About 95% of adult male Labrador Retrievers weigh between 79 and 95 pounds.

• The median weight of adult male Labrador Retrievers is more than 87 pounds.

• The proportion of adult male Labrador Retrievers that weigh less than 80 pounds is approximately equal to the proportion that weigh more 94 pounds.

• Almost all adult male Labrador retrievers weight more than 79 pounds.

• The standardized weights of 80-pound and 94-pound adult male Labrador Retrievers are roughly equal.

Which of the following is true about all Normal distributions?

• There is no area under the curve for z-scores greater than 3.49.

• The area underneath the curve is equal to 1.

• The points at which the curvature changes from “up” to “down” (the points of inflection) are at the first and third quartiles of the distribution.

• About 68% of the values of the variable are more than one standard deviation away from the mean.

• The mean is usually greater than the median

The density curve shown takes the value 0.5 on the interval 0 ≤ x ≤ 2 and takes the value 0 everywhere else. What percent of the observations lie between 0.5 and 1.2?

• 25%

• 35%

• 50%

• 68%

The 16th percentile in a Normal distribution is 25 and 2.5% of the values in the distribution are greater than 40. Which of the following are the best estimates for the mean and standard deviation of the distribution?

• mean ≈ 32.5; standard deviation ≈ 2.5

• mean ≈ 32.5; standard deviation ≈ 5

• mean ≈ 32.5; standard deviation ≈ 10

• mean ≈ 30; standard deviation ≈ 2.5

• mean ≈ 30; standard deviation ≈ 5

A cumulative relative frequency graph for the 48 racers who finished the grueling 50km cross-country ski race at the 2010 Vancouver Olympics is given below.

• 0.17

• 0.40

• 0.45

• 0.50

• 0.55

The distribution of the time it takes for different people to solve a certain crossword puzzle is skewed to the right, with a mean of 30 minutes and a standard deviation of 15 minutes. The distribution of z-scores for those times is

• Normally distributed, with mean 30 and standard deviation 15.

• skewed to the right, with mean 30 and standard deviation 15.

• Normally distributed, with mean 0 and standard deviation 1.

• skewed to the right, with mean 0 and standard deviation 1.

• skewed to the right, but the mean and standard deviation cannot be determined without more information.

Which of the following is closest to the 61st percentile of the standard Normal distribution?

• z = –0.7291

• z = –0.28

• z = 0.20

• z = 0.28

• z = 0.7291

Here is a Normal probability plot for a set of test scores. Which statement is true for these data?

• The data are Normally distributed.

• The data are approximately Normally distributed.

• The data are skewed to the left.

• The data are skewed to the right.

• There is insufficient information to determine the shape of the distribution.

For the density curve shown, which letters correspond to the locations of the mean and median of the distribution?

• Mean = C; Median = B

• Mean = C; Median = C

• Mean = A; Median = B

• Mean = B; Median = B

• Mean = B; Median = A