M408
Statistics
Worksheet 11
Name_______________________________
1.) A set of mathematics exam scores has a mean of 70 and a standard deviation of 8. A set of
English exam scores has a mean of 74 and a standard deviation of 16. For which exam would a
score of 78 have a higher standing? Show all work.
2.) A distribution of scores has a standard deviation of 10. Find the z-scores corresponding to
the following values:
a.
A score 20 points below the mean.
b.
A score 10 points below the mean.
c.
A score 15 points above the mean.
d.
A score 30 points above the mean.
3.) Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT scores is
approximately normal, with mean 500 and standard deviation 100. Gerald takes the ACT
mathematics test and scores 27. ACT scores are normally distributed with mean 18 and standard
deviation 6. Find the z – scores for each student, and determine who has the better test score.
4.) The distribution of major league batting averages has changed over the years, but it always
remains approximately normal. In 1911, Ty Cobb batted .420. In 1941, Ted Williams batted
.406. In 1980, George Brett batted .390. Use the data below to determine which batter did the
best compared to other hitters of their eras. Show all work.
Decade
1910s
1940s
1980s
Mean Batting Average
0.266
0.267
0.261
Standard Deviation
0.0371
0.0326
0.0317
5.) You just scored a 92 on your stats final. Your friend Ethel is bragging that she took the class
last year, and got a 95 on the final. Your teacher tells you that the results are normally
distributed, but the test is slightly different each year.
=3
This Year’s Test  = 85
 = 89
 = 3.5
Last Year’s Test
Use z – scores to decide if Ethel really outperformed you. Show work.
6.) In a population of scores, a raw score with the value of 79 corresponds to a Z of -1.00, and a
raw score of 84.5 corresponds to a Z of +1.75. What is the mean and standard deviation of this
population?
7.) If Ned scores more than 0.8 standard deviations below the mean of his class on the final
assessments, he will not get accepted to the stuffy east-coast school of his dreams. The mean
score on the assessment is 280, and the standard deviation is 22. What is the minimum score that
he can get on the assessment in order to get accepted?