The height of women ages 20-29 is normally distributed, with a mean of 64.9 inches. assume sigmaequals2.3 inches. are you more likely to randomly select 1 woman with a height less than 66 inches or are you more likely to select a sample of 27 women with a mean height less than 66 inches? explain.

To select a sample of 27 women with a mean height less than 66 inches is more likely than to randomly select 1 woman with a height less than 66 inches

Step-by-step explanation:

1) The probability of randomly selecting 1 woman with a height less than 66 inches is

P(z<z(66)) where z(66) is the z-score of the woman whose height is 66 inches.

z score can be calculated using the formula

z(66)= where

Then z(66)= ≈ 0.48

and P(z<0.48) = 0.6844

2) The probability of selecting a sample of 27 women with a mean height less than 66 inches can be calculated using the equation

t= where

t= ≈ 2.49

looking t-table P(t<2.49)≈0.9903

Since 0.9903>0.6844 we can conclude that to select a sample of 27 women with a mean height less than 66 inches is more likely than to randomly select 1 woman with a height less than 66 inches

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