Normal Distributions Homework Solutions printable pdf download

Normal Distributions Homework Solutions

1. Most IQ tests have a mean of 100 and a standard deviation of 15. What percent of the population

has an IQ greater than 130? Between 100 and 130? Greater than 145?

Answers:

p(130 < x) = :02275 = 2:275%

p(100 < x < 130) = 47:8%

p(145 < x) = :00135 = 0:135%

2. Andr Lundberg has devised a di®erent IQ test.

(You can try it yourself at ywq275g/index2.htm)

The mean is 35 and the standard deviation is 9.8. What score on the test in problem 1 corresponds

to a score of 53 on Andr's test?

Answer:

p(53 < x) = :03312 with m = 35 and s = 9:8

Now you need to solve p(a < x) = :033 for a with m = 100 and s = 15: You should get

a = 127:5 approximately.

3. The physics department has three placement tests. On each test the mean is 100. On Test #1 the

standard deviation is 10. On Test #2 the standard deviation is 8, and on Test #3 the standard

deviation is 15.

Rank the following four results:

Student

Test

Score

Sandy

112

Chris

110

Kelly

112

Lou

125

Normal Distributions Homework Solutions