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Ch. 2 Review Sheet

1. 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.

2. Golf courses have a wide range of difficulty. Similarly, players differ in ability. In order to adjust for variations between players, they are often assigned a handicap score. To adjust for variations between courses, a handicapper decides to compare the golfer’s score against the data from the course. Suppose course A plays at a mean score of 76 with a standard deviation of 8 strokes with a normal distribution of scores. The mean score for course B is 80 with a standard deviation of 6 strokes and the scores are normally distributed. If a golfer regularly shoots an 80 on course A, what should be the comparable score on course B?

a) 80

b) 83

c) 84

d) 86

e) 88

3. Rainwater was collected in water collectors at 30 different sites near an industrial basin and the amount of acidity (pH level) was measured. The mean and standard deviation of the values are 4.60 and 1.10, respectively. When the pH meter was recalibrated back at the laboratory, it was found to be in error. The error can be corrected by adding 0.1 pH units to all of the values and then multiply the result by 1.2. The mean and standard deviation of the corrected pH measurements are:

a) 5.64, 1,44

b) 5.64, 1.32

c) 5.40, 1.44

d) 5.40, 1.32

e) 5.64, 1.20

4. 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%

5. A distribution of scores is approximately normal with a mean of 78 and a standard deviation of 8.6. Which of the following equations can be used to find the score x above which 33 percent of the scores fall?

a) [pic]

b) [pic]

c) [pic]

d) [pic]

e) [pic]

6. 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 deviations 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.

7. 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.

8. The length of time a group of 62 students spent on a no-time-limit final exam in Algebra II was recorded. According to these data, the mean time students spent on the exam was 94.1 minutes, and the standard deviation was 24.23 minutes. Suppose the exam proctor realized after compiling these data that he had used the wrong start time in his calculation, so that each value for time spent on exam needs to be reduced by 15 minutes. He also wants to express the times in hours, rather than minutes. Find the mean and standard deviation of the transformed data.

9. In a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. It was determined that the average speed was 42 mph and the standard deviation was 15 mph. In addition, a histogram revealed that vehicle speed at impact is approximately normally distributed.

a) Between what two numbers did the middle 95% of all the recorded speeds fall?

b) What proportion of vehicle speeds were between 30 mph and 55 mph?

c) What proportion of vehicle speeds exceeded 70 mph?

10. The figure below is a density curve.

a) Mark the approximate location of the median. Justify your choice of location.

b) Mark the approximate location of the mean. Justify your choice of location.

c)

11. Below are cumulative frequency graphs for the age distributions of the populations of France and the Philippines.

a) Piper’s 45-year-old uncle lives in France.  In which percentile is Piper’s uncle for age amongst people in France?  Interpret this percentile. 

b) What percentage of the population in the Philippines is between 10 and 20 years old?  Explain how you found your answer.

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