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In: Statistics and Probability

50 years ago, the mean height for women in their 20’s was 62.6 inches. Assume that...

50 years ago, the mean height for women in their 20’s was 62.6 inches. Assume that the heights of today’s women in their 20’s are approximately normally distributed with a standard deviation of 2.88 inches. If the mean height today is the same as that of a halfcentury ago, what percentage of all samples of size 25 today’s women have mean heights of at least 64.24 inches? please show work.

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Expert Solution

Solution :

Given that ,

mean = = 62.6

standard deviation = = 2.88

n = 25

= 62.6

= / n = 2.88 / 25 = 0.576

P( >64.24 ) = 1 - P( < 64.24)

= 1 - P[( - ) / < (64.24 -62.6) /0.576 ]

= 1 - P(z <2.85 )

Using z table

= 1 - 0.9978

= 0.0022

answer= 0.22%

orchestra answered 2 years ago
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