AP STATS - Practice Test

Scientists estimate that the distribution of the life span of the Galápagos Islands giant tortoise is approximately normal with mean 100 years and standard deviation 15 years. Based on the estimate, which of the following is closest to the age of a Galápagos Islands giant tortoise at the 90th percentile of the distribution? a. 80 b. 115 c. 120 d. 125 e. 130

120

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? a. 0.17 b. 0.25 c. 0.36 d. 0.83 e. 0.95

a. 0.17

Question Data on homes recently sold in a certain town included the area of the home, reported in square feet. The table below shows summary statistics of the reported areas, in square feet. An auditor determined that an error was made in the reported areas and that all of the areas should have been 100 square feet greater than what was reported. The areas were corrected and new summary statistics were reported. What are the interquartile range (IQR) and the standard deviation of the corrected areas? a. IQR 102, standard deviation 61.0723 b. IQR 102, standard deviation 161.0723 c. IQR 202, standard deviation 61.0723 d. IQR 202, standard deviation 162.0723 e. IQR 187, standard deviation 61.0723

a. IQR 102, standard deviation 61.0723

Question A graduate student conducted a study of field mice in rural Kansas. The student obtained a sample of 100 field mice and recorded the weight, in grams, of each mouse. After the measurements were taken, it was discovered that the scale was not calibrated correctly. The student adjusted the 100 recorded measurements by subtracting 3 grams from each measurement. Which of the following statistics for the weight, in grams, of the field mice has the same value before and after the adjustment? a. the median b. the mean c. the first quartile d. the third quartile e. the interquartile range

a. the interquartile range

Question Each value in a sample has been transformed by multiplying by 3 and then adding 10. If the original sample had a variance of 4, what is the variance of the transformed sample? a. 4 b. 12 c. 16 d. 22 e. 36

b. 12

The weight of adult male grizzly bears living in the wild in the continental United States is approximately normally distributed with a mean of 500 pounds and a standard deviation of 50 pounds. The weight of adult female grizzly bears is approximately normally distributed with a mean of 300 pounds and a standard deviation of 40 pounds. Approximately, what would be the weight of a female grizzly bear with the same standardized score (z-score) as a male grizzly bear with a weight of 530 pounds? a. 276 pounds b. 324 pounds c. 330 pounds d. 340 pounds e. 530 pounds

b. 324 pounds

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?

b. 779.42

The caffeine content of 8-ounce cans of a 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? a. 1% b. 8% c. 12% d. 16% e. 99%

c. 12%

For a recent season in college football, the total number of rushing yards for that season is recorded for each running back. The mean number of rushing yards for the running backs that season is 790 yards. One running back had 1,637 rushing yards for the season, which is 2.42 standard deviations above the mean number of rushing yards. What is the standard deviation of the number of rushing yards for the running backs that season? a. 250 yards b. 300 yards c. 350 yards d. 400 yards e. 450 yards

c. 350 yards

A data set of test scores is being transformed by applying the following rule to each of the raw scores. Transformed score = 3.5(raw score) + 6.2 Which of the following is NOT true? a. The mean transformed score equals 3.5(the mean raw score) + 6.2 b. The mean transformed score equals 3.5(the mean raw score) + 6.2. c. The range of the transformed scores equals 3.5(the range of the raw scores) + 6.2. d. The standard deviation of the transformed scores equals 3.5(the standard deviation of the raw scores). e. The IQR of the transformed scores equals 3.5(the IQR of the raw scores).

c. The range of the transformed scores equals 3.5(the range of the raw scores) + 6.2.

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? a. the student did better in chemistry b. the student did better in calculus c. the student did equally well in each course d. there is no basis for comparison, since the subjects are different from each e. there is not enough information for comparison, because the number of students in each class is not known.

c. The student did equally well in each course.

Question Administrators at a state university computed the mean GPA (grade point average) for juniors and seniors majoring in either physics or chemistry. The results are displayed in the table below. When juniors and seniors are grouped together, could physics majors have a higher mean GPA than chemistry majors? a. No. The physics majors' mean GPA for juniors and seniors must be 3.0, while the chemistry majors' mean GPA for juniors and seniors must be 3.3. b. No. There is not enough information to determine the mean GPA for each major, but it must be higher for chemistry majors than for physics majors. c. Yes. It could happen. Whether it does happen depends on the number of juniors and seniors in each major d. Yes. It could happen. Whether it does happen depends on the variability of the GPAs within each of the four groups of students. e. Yes. It could happen. Whether it does happen depends on the shapes of the distributions of the GPAs for each of the four groups of students.

c. Yes. It could happen. Whether it does happen depends on the number of juniors and seniors in each major

Which of the following describes a continuous variable? a. the number of items sold at a craft booth for one day b. the number of apps downloaded from a website one day c. the diameters of the tree trunks at an evergreen farm d. the number of baskets made by a basketball player e. the shoe sizes of all shoes on sale at a department store.

c. the diameters of the tree trunks at an evergreen farm

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 had a standardized score of z = 1.72 before the conversion, what is the standardized score for the student after the conversion? a. z = 0.26 b. z = 1.03 c. z - 1.72 d. z = 1.98 e. the standardized score for the student after the conversion cannot be determined.

c. z = 1.72

A sleep time of 15.9 hours per day for a newborn baby is at the 10th percentile of the distribution of sleep times for all newborn babies. Assuming the distribution is normal with standard deviation 0.5 hour, approximately what is the mean sleep time, in hours per day, for newborn babies? a. 15.1 b. 15.3 c. 16.3 d. 16.5 e. 16.7

d. 16.5

In the 1830s, land surveyors began to survey the land acquired in the Louisiana Purchase. Part of their task was to note the sizes of trees they encountered in their surveying. The table of data below is for bur oak trees measured during the survey. Question An outlier may be defined as a data point that is more than 1.5 times the interquartile range below the lower quartile or is more than 1.5 times the interquartile range above the upper quartile. According to this definition, what is the diameter, in inches, of the smallest tree that is an outlier? a. 4 b. 28 c. 30 d. 34 e. 36

d. 34

The distribution of the number of transactions per day at a certain automated teller machine (ATM) is approximately normal with a mean of 80 transactions and a standard deviation of 10 transactions. Which of the following represents the parameters of the distribution? a. x = 80; s = 10 b. x = 80; s^2 = 10 c. x = 80, o = 10 d. u = 80; o = 10 e. u = 80; s = 10

d. u = 80; o = 10

Data will be collected on the following variables. Which variable can be considered discrete? a. the height of a person b. the weight of a person c. the length of a persons arm span d. the time it takes for a person to solve a puzzle e. the number of books a person finished reading last month.

e. the number of books a person finished reading last month.

Height, in meters, is measured for each person in a sample. After the data are collected, all the height measurements are converted from meters to centimeters by multiplying each measurement by 100. Which of the following statistics will remain the same for both units of measure? a. the mean of the height measurements b. the median of the height measurements c. the standard deviation of the height measurements d. the maximum of the height measurements e. the z-scores of the height measurements

e. the z-scores of the height measurements

A distribution of test scores is not symmetric. Which of the following is the best estimate of the z-score of the third quartile? a. 0.67 b. 0.75 c. 1.00 d. 1.41 e. this z-score cannot be estimated from the information given

e. this z-score cannot be estimated from the information given