621 Assume that the height of 1000 students is normally dist

6.21 Assume that the height of 1000 students is normally distributed with mean height of 68 inches and standard deviation of 4 inches. a) Determine the number of students with a height between 64 and 72 inches. b) Find the number of students with a height exceeding the mean height.

Solution

(a) P(64<X<72) = P((64-68)/4 <(X-mean)/s <(72-68)/4)

=P(-1<Z<1) =0.6827 (from standard normal table)

So n= 0.6827*1000 =682.7

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(b)P(X>68) = P(Z>(68-68)/4)

=P(Z>0) = 0.5 (from standard normal table)

So n=1000*0.5 =500