Statistics Normal Calculations

Penny got a z-score of 0.62 on the last AP Statistics test. What does this value mean?

• 62% of students scored less than or equal to Penny on the last AP Statistics test.

• Penny’s score on the test was .62 points higher than the mean of the test.

• Penny’s score is 0.62 standard deviations above the mean on the test.

• Penny got a 62% on the last AP Statistics test.

• The AP Statistics exam has a standard deviation of 0.62 points.

At a small coffee shop, the distribution of the number of seconds it takes for a cashier to process an order is approximately normal with mean 276 seconds and standard deviation 38 seconds. Which of the following is closest to the proportion of orders that are processed in less than 240 seconds?

• 0.17

• 0.25

• 0.36

• 0.83

• 0.95

The caffeine content of 8-ounce cans of certain cola drink is approximately normally distributed with mean 33 milligrams (mg). A randomly selected 8-ounce can containing 35 mg of caffeine is 1.2 standard deviations above the mean. Approximately what percent of 8-ounce cans of the cola have a caffeine content greater than 35 mg?

• 1%

• 8%

• 12%

• 16%

• 99%

On one particular IQ Test the scores are approximately normal with mean 100 pts and standard deviation 15 pts. Based on the estimate, which of the following is closest to the 90th percentile of the distribution of IQ scores?

• 80 points

• 115 points

• 120 points

• 125 points

• 130 points

The distribution of lengths of salmon from a certain river is approximately normal with standard deviation 3.5 inches. If 10 percent of salmon are longer than 30 inches, which of the following is closest to the mean of the distribution?

• 26 inches

• 28 inches

• 30 inches

• 33 inches

• 34 inches

A pregnancy that lasts 245 days is at the 10th percentile. Assuming the distribution of duration of pregnancies is normal with standard deviation 16 days, approximately what is the mean pregnancy duration, in days?

• 224 days

• 266 days

• 270 days

• 277 days

• 279 days

A produce supplier ships boxes of produce to individual customers. The distribution of weights of shipped boxes is approximately normal with mean 36 pounds and standard deviation 4 pounds. Which expression represents the weight, in pounds, at the 75th percentile of the distribution?

• -1.96(4)+36

• -0.25(4) +36

• 0.25(4) +36

• 0.67(4) +36

• 0.75(4) +36

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

• The student did better in chemistry.

• The student did better in calculus.

• The student did equally well in each course.

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

• There is not enough information for comparison, because the number of students in each class is not known.

Some descriptive statistics for a set of test scores are shown above. For this test, a certain student has a standardized score of z= -1.2. What score did this student receive on the test?

• 266.28

• 779.42

• 1008.02

• 1083.38

• 1311.98

Students in a large psychology class measured the time, in seconds, it took each of them to perform a certain task. The times were later converted to minutes. If a student has a standardized score of z=1.72 before the conversion, what is the standardized score for the student after the conversion?

• z= 0.26

• z= 1.03

• z= 1.72

• z= 1.98

• The standardized score for the student after the conversion cannot be determined.