Ch. 2 Review Sheet
1. The state Employment Service of a certain state certifies the typing speed of applicants.
Suppose typing speeds are approximately normally distributed with a mean of 55 words
per minute and a standard deviation of 4 words per minute. If Kim scores at the 95th
percentile, then her typing speed is closest to
a)
b)
c)
d)
e)
47 wpm
50 wpm
59 wpm
62 wpm
63 wpm
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)
b)
c)
d)
e)
80
83
84
86
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)
b)
c)
d)
e)
5.64, 1,44
5.64, 1.32
5.40, 1.44
5.40, 1.32
5.64, 1.20
4. Studies on the subject of how much high school seniors study per week have indicated
that the standard deviation of study time per week is 2.6 hours. Only 10% of the seniors
have study times that exceed 20 hours per week. Find the mean number of hours the high
school seniors study per week. Assume the study times are normally distributed.
5. A sales person ranks in the top 5% of all sales people in a large company. If the annual
mean sales amount is $750,000 and the standard deviation is $150,000, how much does
the person sell each year?
a)
b)
c)
d)
e)
$757,500
$996,750
$1,044,000
$1,697,100
$2,650,500
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)
b)
c)
d)
e)
The mean of the height measurements.
The median of the height measurements.
The standard deviation of the height measurements.
The maximum of the height measurements.
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.