Statistics Trivia Questions Test: Advanced Placement Exam

1. A department store has a promotion in which it hands out a "scratchcard" at the checkout register, with a percent discount concealed by an opaque covering. The customer scratches off the covering and reveals the amount of the discount. The table below shows the probability that a randomly selected card contains each percent discount. What is the expected value of the percentage of discount?

Percentage Discount	5%	10%	15%	25%	50%
Probability	0.45	0.25	0.15	0.10	0.05

5%

12%

15%

21%

40%

The expected value of the percentage of discount can be calculated by multiplying each percentage discount by its corresponding probability, and then summing up these values. In this case, the calculation would be: (0.05 * 0.45) + (0.10 * 0.25) + (0.15 * 0.15) + (0.25 * 0.10) + (0.50 * 0.05) = 0.0125 + 0.025 + 0.0225 + 0.025 + 0.025 = 0.11 or 11%. Therefore, the correct answer of 12% is incorrect.

Explanation

The expected value of the percentage of discount can be calculated by multiplying each percentage discount by its corresponding probability, and then summing up these values. In this case, the calculation would be: (0.05 * 0.45) + (0.10 * 0.25) + (0.15 * 0.15) + (0.25 * 0.10) + (0.50 * 0.05) = 0.0125 + 0.025 + 0.0225 + 0.025 + 0.025 = 0.11 or 11%. Therefore, the correct answer of 12% is incorrect.

2. Breakfast cereals have a wide range of sugar content. Some cereals contain High Fructose Corn Syrup (HFCS) as a source of sugar and some do not. The boxplots below show the total sugar content of different types of cereal for those containing HFCS and for those that do not. Which statement is true based on the boxplots?

The number of cereals with HFCS is about the same as the number of cereals without HFCS.

The cereals with HFCS have a greater interquartile range than the cereals without HFCS.

The cereals without HFCS have a greater range than the cereals with HFCS.

About half the cereals without HFCS have less sugar than about three-fourths of the cereals with HFCS.

About half the cereals with HFCS have more sugar than about three-fourths of the cereals without HFCS.

Based on the boxplots, we can observe that the median sugar content of cereals with HFCS is higher than the median sugar content of cereals without HFCS. Additionally, the upper quartile of cereals with HFCS is higher than the upper quartile of cereals without HFCS. This means that about half of the cereals with HFCS have more sugar than about three-fourths of the cereals without HFCS. Therefore, the statement "About half the cereals with HFCS have more sugar than about three-fourths of the cereals without HFCS" is true based on the boxplots.

Explanation

Based on the boxplots, we can observe that the median sugar content of cereals with HFCS is higher than the median sugar content of cereals without HFCS. Additionally, the upper quartile of cereals with HFCS is higher than the upper quartile of cereals without HFCS. This means that about half of the cereals with HFCS have more sugar than about three-fourths of the cereals without HFCS. Therefore, the statement "About half the cereals with HFCS have more sugar than about three-fourths of the cereals without HFCS" is true based on the boxplots.

3. For the 176 players on the rosters of NBA teams for one season, the third quartile for the total number of offensive rebounds for one season was 143. If five players are selected at random (with replacement) from that season, what is the approximate probability that at least three of them had more than 143 rebounds that season?

0.0127

0.0879

0.1035

0.8965

0.9121

The given question asks for the approximate probability that at least three out of five randomly selected players had more than 143 rebounds in a season where the third quartile for the total number of offensive rebounds was 143. To solve this, we can use the binomial probability formula. The probability of at least three players having more than 143 rebounds can be calculated by finding the probability of exactly three, exactly four, and exactly five players having more than 143 rebounds, and then summing them up. The approximate probability of this event is 0.1035.

Explanation

The given question asks for the approximate probability that at least three out of five randomly selected players had more than 143 rebounds in a season where the third quartile for the total number of offensive rebounds was 143. To solve this, we can use the binomial probability formula. The probability of at least three players having more than 143 rebounds can be calculated by finding the probability of exactly three, exactly four, and exactly five players having more than 143 rebounds, and then summing them up. The approximate probability of this event is 0.1035.

4. Researchers were gathering data on alligators in an attempt to estimate an alligator's weight from its length. They captured 29 alligators and measured their length and weight. They created three regression models. Each model, along with its residual plot, is shown below. y represents the weight in pounds and x represents the length in inches. Which statement below is true?

There is a linear relationship between weight and length, and Model I is most appropriate.

There is a linear relationship between weight and length, and Model II is most appropriate.

There is a non-linear relationship between weight and length, and Model I is most appropriate.

There is a non-linear relationship between weight and length, and Model II is most appropriate.

There is a non-linear relationship between weight and length, and Model III is most appropriate.

The residual plot for Model II shows a clear pattern of a curved line, indicating a non-linear relationship between weight and length. This suggests that as the length of the alligator increases, the rate at which its weight increases also changes. Model II is the most appropriate because it captures this non-linear relationship more accurately than the other models.

Explanation

The residual plot for Model II shows a clear pattern of a curved line, indicating a non-linear relationship between weight and length. This suggests that as the length of the alligator increases, the rate at which its weight increases also changes. Model II is the most appropriate because it captures this non-linear relationship more accurately than the other models.

5. A high school sent a survey to a randomly selected sample of 75 of last year's graduating class. 27 of those selected did not return the survey. The best plan of action would be to:

Use the surveys that were returned and change the sample size to 48 for the analysis.

Use the surveys that were returned and leave the sample size at 75 for the analysis.

Randomly select 27 additional class members and send the survey to them.

Start over with a new sample but use a larger sample size.

Follow up with those that did not return the survey and encourage them to respond.

The best plan of action would be to follow up with those who did not return the survey and encourage them to respond. This is because the sample size of 75 was randomly selected, and the non-response rate of 27 out of 75 is quite high. By following up and encouraging non-respondents to participate, the response rate can be increased, ensuring a more representative sample for the analysis. Using the surveys that were returned and leaving the sample size at 75 may introduce bias and may not accurately reflect the views and opinions of the entire graduating class.

Explanation

The best plan of action would be to follow up with those who did not return the survey and encourage them to respond. This is because the sample size of 75 was randomly selected, and the non-response rate of 27 out of 75 is quite high. By following up and encouraging non-respondents to participate, the response rate can be increased, ensuring a more representative sample for the analysis. Using the surveys that were returned and leaving the sample size at 75 may introduce bias and may not accurately reflect the views and opinions of the entire graduating class.