AP Statistics Chapter 2

The lifetime of a 9-volt battery in constant use has an approximately Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. Which of the following is the approximate lifetime of a battery that lasts longer than 90% of all batteries?

• 541.6 hours

• 517.28 hours

• 490.4 hours

The lifetime of 9-volt battery in constant use has an approximately Normal distribution with a mean of 516 hours and a standard deviation of 20 hours. Which of the following best describes the distribution of standard scores for the lifetimes of such batteries?

• Exactly Normal, with mean 0 and standard deviation 1

• Approximately Normal, with mean 0 and standard deviation 1

• Approximately Normal, with mean 1 and standard deviation 1.

Fuji apples grown at a certain orchard have a mean weight of 5.2 ounces with a standard deviation of 0.8 ounces. Suppose the scale the orchard owner uses systematically underweighs apples by 0.2 ounces and also weighs the apples in grams, rather than ounces. What would the mean and standard deviation of these apples’ weights be as determined by this scale? (Note: 1 ounce ≈ 28 grams).

• Mean 145.6 grams, standard deviation 22.4 grams.

• Mean 140 grams, standard deviation 22.4 grams.

• Mean 140 grams, standard deviation 16.8 grams.

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 0.2 and 1.6?

• 25%

• 35%

• 50%

• 68%

• 70%

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

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

A machine fills plastic bottles with mineral water. The volume of mineral water that the machine pours into each bottle follows a normal distribution with the mean of 498ml and a standard deviation of 3.4ml. Each bottle has a maximum capacity of 506ml. On the label of each bottle is printed the statement: Contents 500ml.

Find the probability that a bottle chosen by random has a volume less than 500 ml

• 0.278

• -0.278

• 0.722

• 0.498

In 1970, the mean price of a new car was $3250 and the standard deviation was 1,500. In 2012, the mean was $40,250 and the standard deviation was $12,000. If a Ford Mustang cost $2700 in 1970 and $37,000 in 2012, in which year was it more expensive relative to other cars?

• 1970, because the standardized score is greater than in 2012.

• 1970, because the standard deviation is smaller.

• 2012, because the standardized score is greater than in 1970

• 2011, because $37,000 is greater than $3,250.

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

The weights of adult female Chihuahua are approximately Normally distributed with a mean of 50 pounds and a standard deviation of 5 pounds. Which of the following statements is true?

• About 95% of adult female Chihuahua weigh between 45 and 55 pounds.

• The median weight of adult female Chihuahua is more than 55 pounds.

• The proportion of adult female Chihuahua that weigh less than 45 pounds is approximately equal to the proportion that weigh more 55 pounds.

• Almost all adult female Chihuahua weight more than 60 pounds.

• The standardized weights of 45-pound and 94-pound adult female Chihuahua are roughly equal.

Which of the following is/are not 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.