Name________________________
Period____ Date_______________
Classwork Ch. 4.4
AP STATS
Normal Distributions/ Empirical Rule
1. The height of young American women has an approximately normal distribution with mean µ= 65.5 inches and
standard deviation σ= 2.5 inches.
A. Sketch the Normal Model and clearly label the 68-95-99.7 Rule.
Find the relative frequencies (proportion) of each of the following:
B. A woman is below 68” tall
C. a woman is above 60.5” tall
D. A woman is between 63 and 68 inches tall.
E. A woman is between 58 and 70.5 inches tall.
2. The Chapin Social Insight Test evaluates how accurately someone appraises other people. Scores are approximately
normally distributed with mean µ= 25 and standard deviation σ= 5. The range of possible scores is 0 to 41.
A. Sketch the Normal Model and clearly label the 68-95-99.7 Rule.
B. What percentage of the population has scores below 20?
C. What percentage of the population has scores above 35?
D. What percentage of the population has scores between 20 and 30?
E. What percentage of the population has scores above 25?
F. What percentage of the population has scores below 10?
3. The Graduate Record Exam (GRE) is widely used to help predict the performance of applicants to graduate school. The
range of possible scores on the each proportion of the test is 200 to 800. A university finds that the scores of its
applicants on the quantitative proportion of the GRE are approximately normal with mean µ= 544 and standard
deviation σ= 103.
A. Find the probability that a randomly selected score is more than 647.
B. Would you be skeptical of a reported score less than 235? Why?
4. The distribution of the heights of students in a large elementary school class is roughly Normal. Moreover, the average
height is 45 inches, and approximately 95% of the heights are between 41 and 49 inches. Find the standard deviation
of the distribution of heights.
5. On a history test with a mean of 80 and a standard deviation of 5, Lisa scored 88. On an English test with a mean of
50 and a standard deviation of 10, Bruce scored 66. Who did better, relative to students taking the same test?
6.
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 that course A plays at a mean
score of 72 with a standard deviation of 10 strokes with an approximately normal distribution of scores. The mean
score for course B is 84 with a standard deviation of 12 strokes and the scores are also approximately normally
distributed. If a golfer regularly shoots an 85 on course A, what should be the comparable score on course B?
7.
Following a dramatic drop of 500 points in the Dow Jones Industrial Average in September 1998, a poll
conducted for the Associated Press found that 92% of those polled said that a year from now their family
financial situation will be as good as it is today or better. The number 92% is a
A Statistic
B Sample
C Parameter
D Population
E None of the these.
Anwers:
1b) .84 c) .975 d) .68 e) .9735 2b) .16 c) .025 d) .68 e) .50 f) .0015 3a) .16 b) yes. More
than 3 sd away from mean. This happens less than .15% of time. 4) 2 5) Z=1.6 They did the same.
6) 99.6, so approx. 100. 7) A