A population of children has normally distributed heights with amean of 39 inche

Question

A population of children has normally distributed heights with amean of 39 inches and a SD of 2 inches.

a. What is the probability that a randomly chosen child will have aheight between 38 and 40 inches?

b. Over 40 inches?

c. Between what 2 values(symmetrically distributed around the mean)will 90% of the heights of children fall?

Explanation / Answer

   Let X ~ N( 39 , 2 )    Then :    Z = ( X - 39 ) /2                      Z ~ N( 0 ,1 )    a)   P[ 38 40 ]   = P[ ( X - 39 ) / 2 > ( 40 - 39 ) /2 ]                                = P[   Z > 1/2 ]                                 = 0.3085               ............using tables c) To find c such that :    P[ -c the 2 values are 39 - 3.29 = 35.71    and   39 +3.29 = 42.29

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