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AP Stats: Unit 4 test (multiple choice)

Last updated about 1 month ago

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Question 1

1.

The commuting time for a student to travel from home to a college campus is normally distributed with a mean of 30 minutes and a standard deviation of 5 minutes. If the student leaves home at 8:25 A.M., what is the probability that the student will arrive at the college campus later than 9 A.M.?

1.00

0.84

0.32

0.16

0.50

Question 2

2.

For a certain population of penguins, the distribution of weight is approximately normal with a mean of 15.1 kilograms and standard deviation 2.2 kg. Approximately what percent of the penguins from the population have a weight between 13.0 kg and 16.5 kg?

74%

57%

17%

68%

34%

Question 3

3.

A candy company produces individually wrapped candies. The quality control manager for the company believes that the weight of the candies is approximately normally distributed with a mean of 720 milligrams (mg). If the manager’s belief is correct, which of the following intervals of weights will contain the largest proportion of the candies in the distribution of weights?

740 mg to 780 mg

700 mg to 740 mg

680 mg to 720 mg

660 mg to 700 mg

620 mg to 660 mg

Question 4

4.

The number of tickets purchased by a customer for a musical performance at a certain concert hall can be considered a random variable. The table below shows the relative frequency distribution for the number of tickets purchased by a customer.
Suppose each ticket for a certain musical performance costs $12. Based on the distribution shown, what is the mean cost per customer for the performance?

$29.40

$36.00

$24.50

$2.45

$2.75

Question 5

5.

A box contains 10 tags, numbered 1 through 10, with a different number on each tag. A second box contains 8 tags, numbered 20 through 27, with a different number on each tag. One tag is drawn at random from each box. What is the expected value of the sum of the numbers on the two selected tags?

15.0

29.0

13.5

27.0

14.5

Question 6

6.

The probability of obtaining a head when a certain coin is flipped is about 0.65. Which of the following is closest to the probability that heads would be obtained 15 or fewer times when this coin is flipped 25 times?

0.60

0.37

0.65

0.14

0.39

Question 7

7.

A blind taste test will be conducted with 9 volunteers to determine whether people can taste a difference between bottled water and tap water. Each participant will taste the water from two different glasses and then identify which glass he or she thinks contains the tap water. Assuming that people cannot taste a difference between bottled water and tap water, what is the probability that at least 8 of the 9 participants will correctly identify the tap water?

0.9805

0.0020

0.8889

0.9980

0.0195

Question 8

8.

It is known that 75 percent of all households in the United States have intermittent Internet connectivity problems. For random samples of 450 independent households in the United States, what are the mean and standard deviation of the distribution of the number of households that have intermittent Internet connectivity problems?

\mu=450(0.25) \; \sigma=\sqrt{450(0.25)(0.75)}

\mu=450(0.75) \; \sigma=\sqrt{450(0.75)(0.25)}

\mu=450(0.25)(0.75) \; \sigma=\sqrt{450(0.25)(0.75)}

\mu=(0.75) \; \sigma=\sqrt{\frac{(0.25)(0.75)}{450}}

\mu=450(0.25)(0.75) \; \sigma=\sqrt{\frac{(0.25)(0.75)}{450}}

Question 9

9.

In a certain board game, a player rolls two fair six-sided dice until the player rolls doubles (where the value on each die is the same). The probability of rolling doubles with one roll of two fair six-sided dice is \frac{1}{6}.
What is the probability that it takes three rolls until the player rolls doubles?

(\frac{5}{6})^3

(\frac{5}{6})(\frac{1}{6})^2

(\frac{1}{6})(\frac{5}{6})^3

(\frac{1}{6})(\frac{5}{6})^2

(\frac{1}{6})^3

Question 10

10.

Ming is learning the game of tennis and will practice serving a tennis ball within bounds. Assume that the probability of Ming serving a tennis ball within bounds is 0.40 and that her serves are independent of each other.
What is the probability that the first time Ming serves a tennis ball within bounds will occur on her 4th attempt?

0.4

1-(0.4)^4

(0.6)^3\,(0.4)

\binom{4}{1}(0.4)(0.6)^{3}+\binom{4}{1}(0.4)^{2}(0.6)^{2}+\binom{4}{1}(0.4)^{3}(0.6)

\binom{4}{1}(0.4)(0.6)^3

Question 11

11.

An engineering student collected data on the maximum height, in feet, and maximum speed, in miles per hour, of thirteen roller coasters. A scatterplot of the data and the least-squares regression line are shown. The maximum heights of five of the roller coasters are 60, 105, 150, 200, 215 feet.
If the least-squares regression line is used to predict the maximum speed for the five roller coasters, for which maximum height, in feet, would the absolute value of the residual be largest?

105

215

60

200

150

Question 12

12.

A data scientist had different sets of data. For each data set, the scientist fit a least-squares regression line, then graphed the residuals versus the predicted values for each. Which residual plot indicates that the least-squares regression model was the most appropriate model to fit the data?

Question 13

13.

A jewelry manufacturer tracks sales of three types of jewelry (rings, necklaces, and earrings) across each of three different retail outlet categories (specialty store, department store, and warehouse club). The segmented bar chart shows the distribution for each retail outlet for the three jewelry types based on sales data for the past week.
Based on the chart, which statement must be true?

The number of earring sales for department stores was the same as the number of earring sales for warehouse clubs.

For each retail outlet category, less than 30% of sales were earrings.

The greatest number of ring sales came from warehouse clubs.

The number of ring sales for specialty stores was greater than the number of ring sales for warehouse clubs.

The percent of earring sales at department stores was less than the percent of necklace sales at specialty stores.

Question 14

14.

A random sample of 374 United States pennies was collected, and the age of each penny was determined. According to the boxplot below, what is the approximate interquartile range (IQR) of the ages?

16

50

10

8

40

Question 15

15.

An independent polling agency was hired to track the preferences of registered voters in a district for an upcoming election. The polling agency divided the district into twenty regions and believes that the regions are similar to one another in their composition. The agency then randomly selected two of the regions and surveyed all registered voters in both regions.
Which of the following best describes the sampling method used by the polling agency?

Convenience sampling

Stratified random sampling

Cluster Sampling

Simple random sampling

Systematic sampling