Density Curves Review

Jorge’s score on Exam 1 in his statistics class was at the 64th percentile of the scores for all students. His score falls1.

• between the minimum and the first quartile.

• between the first quartile and the median.

• between the median and the third quartile.

• between the third quartile and the maximum.

• at the mean score for all students.

When Sam goes to a restaurant, he always tips the server $2 plus 10% of the cost of the meal. If Sam’s distribution of meal costs has a mean of $9 and a standard deviation of $3, what are the mean and standard deviation of the distribution of his tips?

• $2.90, $0.30

• $2.90, $2.30

• $9.00, $3.00

• $11.00, $2.00

• $2.00, $0.90

Scores on the ACT college entrance exam follow a bell-shaped distribution with mean 18 and standard deviation 6. Wayne’s standardized score on the ACT was −0.5. What was Wayne’s actual ACT score?

• 5.5

• 12

• 15

• 17.5

• 21

George has an average bowling score of 180 and bowls in a league where the average for all bowlers is 150 and the standard deviation is 20. Bill has an average bowling score of 190 and bowls in a league where the average is 160 and the standard deviation is 15. Who ranks higher in his own league, George or Bill?

• Bill, because his 190 is higher than George’s 180.

• Bill, because his standardized score is higher than George’s.

• Bill and George have the same rank in their leagues, because both are 30 pins above the mean.

• George, because his standardized score is higher than Bill’s.

• George, because the standard deviation of bowling scores is higher in his league.

The number of absences during the fall semester was recorded for each student in a large elementary school. The distribution of absences is displayed in the following cumulative relative frequency graph.

Question: What is the interquartile range (IQR) for the distribution of absences?

• 1

• 2

• 3

• 5

• 14

The number of absences during the fall semester was recorded for each student in a large elementary school. The distribution of absences is displayed in the following cumulative relative frequency graph.

Question: If the distribution of absences was displayed in a histogram, what would be the best description of the histogram’s shape?

• Symmetric

• Uniform

• Skewed left

• Skewed right

• Cannot be determined

Two measures of center are marked on the density curve shown. Which of the following is correct?

• The median is at the yellow line and the mean is at the red line.

• The median is at the red line and the mean is at the yellow line.

• The mode is at the red line and the median is at the yellow line.

• The mode is at the yellow line and the median is at the red line.

• .

  The mode is at the red line and the mean is at the yellow line.

The weights of laboratory cockroaches follow a Normal distribution with mean 80 grams and standard deviation 2 grams. The following figure is the Normal curve for this distribution of weights.

Question: Point C on this Normal curve corresponds to

• 84 grams.

• 82 grams.

• 78 grams.

• 76 grams.

• 74 grams.

The weights of laboratory cockroaches follow a Normal distribution with mean 80 grams and standard deviation 2 grams. The following figure is the Normal curve for this distribution of weights.

Question: About what percent of the cockroaches have weights between 76 and 84 grams?

• 99.7%

• 95%

• 68%

• 47.5%

• 34%

The weights of laboratory cockroaches follow a Normal distribution with mean 80 grams and standard deviation 2 grams. The following figure is the Normal curve for this distribution of weights.

Question: About what proportion of the cockroaches will have weights greater than 83 grams?

• 0.0228

• 0.1587

• 0.0772

• 0.9332

• 0.0668