For children in a certain age range heights are normally dis

For children in a certain age range, heights are normally distributed with a mean of 49 inches and a standard deviation of 3.5 inches. If one child in this age range is selected at random, whats the probability that:

A . He/she will be over 54 inches tall?

b. He/she will be between 47.5 and 51 inches tall?

Solution

A . He/she will be over 54 inches tall?

P(X>54) = P((X-mean)/s >(54-49)/3.5)

=P(Z>1.43) =0.0764 (from standard normal table)

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b. He/she will be between 47.5 and 51 inches tall?

P(47.5<X<51) = P((47.5-49)/3.5<Z<(51-49)/3.5)

=P(-0.43<Z<0.57) =0.3821 (from standard normal table)