AP Stats Normal Distribution Practice

A different species of cockroach has weights that are approximately Normally distributed with a mean of 50 grams. After measuring the weights of many of these cockroaches, a lab assistant reports that 14% of the cockroaches weigh more than 55 grams. Based on this report, what is the approximate standard deviation of weight for this species of cockroaches?

• 4.6

• 5.0

• 6.2

• 4.0

• Cannot determine without more information

A company determines the mean and standard deviation of the employees' salaries in one year. What is the best description of the standard deviation?

• Approximately the median distance between the individual salaries of employees and the mean of every employee's salary.

• The amount of money separating the highest salary from the lowest salary when considering the middle 50% of the distribution.

• The amount of money separating the highest salary from the lowest salary when considering all employees.

• The distance between the salary of an employee and the mean salary of all the employees.

• Approximately the mean distance between the individual salaries of employees and the mean of all employees' salaries.

The heights of adult women are approximately normally distributed about a mean of 65 inches with a standard deviation of 2 inches. If Bella is at the 87th percentile in height for adult women, then her height, in inches, is closest to

• 63

• 67

• 66

• 72

• 70

Andrea's doctor told her that the standardized score (z-score) for her systolic blood pressure, as compared to the blood pressure of other women her age, is 1.75. Which of the following is the best interpretation of this standardized score?

• Andrea's systolic blood pressure is 175.

• Andrea's systolic blood pressure is 1.75 standard deviations above the average systolic blood pressure of women her age.

• Andrea's systolic blood pressure is 1.75 above the average systolic blood pressure of women her age

• Only 1.75% of women Andrea's age have a higher systolic blood pressure than she does.

• Andrea's systolic blood pressure is 1.75 times the average systolic blood pressure of women her age.

At a college the scores on the Spanish final exam are approximately normally distributed, with a mean of 75 and a standard deviation of 12. The scores on the Humanities final are also approximately normally distributed, with a mean of 80 and a standard deviation of 8. A student scored 81 on the Spanish final and 84 on the Humanities final. Relative to the students in each respective class, in which subject did this student do better?

• The student did better in Spanish.

• The student did better in Humanities.

• There is no basis for comparison, since the subjects are different from each other and are in different departments.

• The student did equally well in each course.

• There is not enough information for comparison.

The boys and girls basketball teams at a high school had their heights measured at practice. The following data was recorded for their heights. What can you conclude from the distributions?

• The girls have a larger median and a larger range in heights.

• The boys had a smaller median height than the girls; however, the boys had a larger range of heights.

• The median height for the boys and the girls is the same; however, the girls have a larger range.

• The median height for the boys is larger; however, the girls have a larger range.

• No information can be concluded from the distribution since there is no key included.

A cosmetics supplier ships boxes of highlighter to individual customers. The distribution of weights of shipped boxes is approximately normal with mean 5 pounds and standard deviation 1.2 pounds. Which expression represents the weight, in pounds, at the 75th percentile of the distribution?

• -1.96(1.2) + 5

• -0.25(1.2) + 5

• 0.25(1.2) + 5

• 0.67(1.2) + 5

• 0.75(1.2) + 5

The distribution of scores on the math section of the SAT (out of 800) follows an approximately Normal distribution with a mean of 508 and standard deviation of 110. What percent of students score between 398 and 728 points?

• about 81.5%

• about 50%

• about 83.85%

• about 95%

• about 68%

The 40 yards sprint times for a soccer team are found to be normally distributed with a mean of 5.2 seconds and a standard deviation of 0.3 seconds. What is the approximate z-score for a player who runs a time of 5.6 seconds?

• -1.33

• 1.33

• 0.88

• 1.02

The mean GPA of students in a course at UCDavis is 3.2 with a standard deviation of 0.3. If the distribution of grades at UCDavis is approximately normal, what percent of students in the course have a GPA above 2.9?

• 81.5%

• 84%

• 68%

• 95%