The height of an adult male in the United States is approximately normally distr

Question

The height of an adult male in the United States is approximately normally distributed with a mean of 69.3 inches and a standard deviation of 2.8 inches.

Assume that such an individual is selected at random. What is the probability that his height will be less than 66.7 inches?

Round your answer to 4 decimal places.

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The height of an adult male in the United States is approximately normally distributed with a mean of 69.3 inches and a standard deviation of 2.8 inches.

Find the percentile P83 for the heights of adult males in the United States.

Provided your answer in inches, rounded to 2 decimal places.

Explanation / Answer

Q1.

Mean ( u ) =69.3
Standard Deviation ( sd )=2.8
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 66.7) = (66.7-69.3)/2.8
= -2.6/2.8= -0.9286
= P ( Z <-0.9286) From Standard Normal Table
= 0.1766                  

Q2.

P ( Z < x ) = 0.83
Value of z to the cumulative probability of 0.83 from normal table is 0.954
P( x-u/s.d < x - 69.3/2.8 ) = 0.83
That is, ( x - 69.3/2.8 ) = 0.95
--> x = 0.95 * 2.8 + 69.3 = 71.97                

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