The mean height of women in a country ages 2029 is 644 inche

The mean height of women in a country ages 20-29 is 64.4 inches a random sample of 60 women in this age group is selected .what is the probability that the mean height for the sample is greater than 65 inches if the standard deviation is 2.81

what is the probability that the mean height for the sample is greater than 65 inches?

Solution

Mean height of women in a country aged 20-29 is 64.4 inches.
A random sample of 60 women in this age group is selected.
The standard deviation is 2.81.
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z(65) = (65-64.4)/[2.81/sqrt(60)] = 0.6/(0.3628) = 1.65

P(x-bar > 65) = P(z > 1.65) = 1 - 0.9505 = 0.0495