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# Normal Probability problems

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Assume that the population of heights of male college students is approximately normally distributed with a mean "m" of 68 inches and standard deviation "s" of 3.75 inches. A random sample of 16 heights is obtained:

1.) Describe the distribution of x, height of the college student.

2.) Find the proportion of male college students whose height is greater than 70 inches.

3.) Describe the distribution of x, the mean of samples of size 16.

4.) Find the mean and standard error of the x distribution.

5.) Find P(X>70)

Given x~n(68, 3.75)
P(X>70) = P(Z > 70-68/3.75) = P(Z>-0.53)
P(X>70) = 0.7019

6.) Find P(X<67)

Given x~n(68, 3.75)
P(X<67) = P(Z < 67-68/3.75) = P(Z<-0.26)
P(X<67) = 0.6026

https://brainmass.com/statistics/probability/normal-probability-problems-227023

#### Solution Preview

Statistics Normal Distribution
Assume that the population of heights of male college students is approximately normally distributed with a mean "m" of 68 inches and standard deviation "s" of 3.75 inches. A random sample of 16 heights is obtained:

1.) Describe the distribution of x, height of the college student. ...

#### Solution Summary

The solution provides step by step method for the calculation of probability for normal distribution . Formula for the calculation and Interpretations of the results are also included.

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