Stats chapter 2

*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?

12%

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) 35

E- 36

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? a) 26 b) 28 c) 30 d) 33 e) 34

A- 26

At a photography contest, entries are scored on a scale from 1 to 100. At a recent contest with 1,000 entries, a score of 68 was at the 77thpercentile of the distribution of all the scores. Which of the following is the best description of the 77th percentile of the distribution? a) There were 770 entries with a score less than or equal to 68. b) There were at least 230 entries with a score of 77. c) There were 23% of the entries with a score less than or equal to 68. d) There were 77% of the entries with a score equal to 68. e) There were at least 77% of the entries with a score greater than 68.

A- There were 770 entries with a score less than or equal to 68.

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

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 median transformed score equals 3.5(the median 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.

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 person's 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

Nyasha's financial literacy project involved comparing the annual sales of companies in Canada and companies in the United States that produce software. Using the ratio of 1 Canadian dollar to 0.75 United States dollar, she converted all annual sales from the Canadian companies into United States dollars. For which of the following will the value of the statistic for the annual sales in Canadian dollars be equal to the value of the corresponding statistic in United States dollars? a) The median annual sales b) The standard deviation of the annual sales c) The standardized score of the minimum annual sales d) The mean annual sales e) The interquartile range of the annual sales

C- The standardized score of the minimum annual sales

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.

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

The height of 3-year-old boys is approximately normally distributed. Duncan and Shane are 3-year-old boys.Duncan is 32.0 inches tall and is at the 32nd percentile of the distribution. Shane is 34.0 inches tall and is at the 62nd percentile of the distribution. Which of the following is closest to the mean of the height distribution? a) 32.50 b) 32.79 c) 33.00 d) 33.21 e) 36.53

D- 33.21

Athletes in a particular sport are classified as either offense or defense. The distribution of weights for the athletes classified as offense is approximately normal, centered at 200 pounds, and ranges from 150 pounds to 250 pounds. The distribution of weights for the athletes classified as defense is approximately normal, centered at 300 pounds, and ranges from 250 pounds to 350 pounds. There are 1,000 athletes in each classification. Which of the following is the best description of a histogram of the weights of all 2,000 athletes? a) Skewed to the right (positively skewed) b) Skewed to the left (negatively skewed) c) Approximately uniform and centered at 250 pounds d) Approximately normal and centered at 250 pounds e) Bimodal

E- Bimodal

The distribution of heights of 6-year-old girls is approximately normally distributed with a mean of 46.0 inches and a standard deviation of 2.7 inches. Aliyaah is 6 years old, and her height is 0.96 standard deviation above the mean. Her friend Jayne is also 6 years old and is at the 93rd percentile of the height distribution. At what percentile is Aliyaah's height, and how does her height compare to Jayne's height? a) Aliyaah's height is at the 17th percentile of the distribution, and she is shorter than Jayne. b) Aliyaah's height is at the 67th percentile of the distribution, and she is shorter than Jayne. c) Aliyaah's height is at the 67th percentile of the distribution, and she is taller than Jayne. d) Aliyaah's height is at the 83rd percentile of the distribution, and she is shorter than Jayne. e)Aliyaah's height is at the 83rd percentile of the distribution, and she is taller than Jayne.

D- Aliyaah's height is at the 83rd percentile of the distribution, and she is shorter than Jayne.

The distribution of the weights of loaves of bread from a certain bakery follows approximately a normal distribution. Based on a very large sample, it was found that 10 percent of the loaves weighed less than 15.34 ounces, and 20 percent of the loaves weighed more than 16.31 ounces. What are the mean and standard deviation of the distribution of the weights of the loaves of bread? a) µ = 15.82, σ = 0.48 b) µ = 15.82, σ = 0.69 c) µ = 15.87, σ = 0.50 d) µ = 15.93, σ = 0.46 e) µ = 16.00, σ = 0.50

D- µ = 15.93, σ = 0.46

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 measurement 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.

The commuting time for a student to travel from home to a college campus is normally distributed with a mean of 30 minutes and a standard deviation of 5 minutes. If the student leaves home at 8:25 A.M., what is the probability that the student will arrive at the college campus later than 9 A.M.? a) 0.16 b) 0.32 c) 0.50c d) 0.84 e) 1.00

a) 0.16

The amount of time required for each of 100 mice to navigate through a maze was recorded. The histogram below shows the distribution of times, in seconds, for the 100 mice. Which of the following values is closest to the standard deviation of the 100 times? a) 2.5 sec b) 10 sec c) 20 sec d) 50 sec e) 90 sec

b) 10 sec