Normal Distribution Problems
1. What is the area under the standard normal curve for the following
z-scores?
z-score Area
a. 0.00 to +0.75 0.2734
b. 0.00 to -0.37
c. -0.67 to 1.25
d. 0.35 to 1.67
2. Assume that the mean of a normal distribution of 8,500 scores is 102
and the standard deviation is 18. What score would a student have to receive
so that 90 percent of the scores would be lower?
3. What would be the centile rank of a score of 90 in the distribution
of the previous problem?
4. The 500 members of the freshman class at a university have completed
an English placement examination. Assume the scores are normally distributed,
a mean of 72 and standard deviation of 10. Determine the following:
a. Number of students who achieved a score of 88 or above
b. Number of students who scored less than 60
c. 75th centile
d. 30th centile
e. CR of a score of 75
f. CR of a score of 65
Assume a normal distribution for questions 5-9. :
5. S.A.T. scores have a mean of 500 and a standard deviation of 100.
What percent of high school seniors can be expected to get a score between
575-675?
6. Records indicate that the average life of TV tubes is 3 years with
a standard deviation of 1.5 years. If 100 tubes are sold, how many should
still be working after 1 year?
7. The average seasonal rainfall in a certain town is 18.5 inches with
a standard deviation of 6.5 inches. In how many years out of a period of
50 years would be expected between 15 and 25 inches of rain?
8. Factory A pays an average wage of $4.60 an hour with a standard deviation
of $.30. What percent of workers receive wages between $4.00 and $4.50?
9. An instructor decides to give 10% of his class A's; 20% B's; 40% C's;
20% D's and 10% F's. If the class exam has a mean of 60 and a standard
deviation of 5, what are the score limits for each grade level?
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