Assume that the heights of men are normally distributed with

Assume that the heights of men are normally distributed with a mean of 67.9 inches and a standard deviation of 2.8 inches. Find the probability that a randomly selected man will have a height greater than 68.9 inches: __________. If 64 men are randomly selected, find the probability that the sample has a mean height greater than 68.9 inches: _________.

Solution

mu =67.9

sigma = 2.8

P(X>68.9) = P(Z>) = P(Z>0.3571)

=0.5-0.1406

= 0.3594

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For n =64 std error =2.8/8 = 0.35

P(X>68.9) = P(Z>)=

P(Z>2.857)=0.5-0.4979

= 0.0021