Question

the height of women ages 20-29 is normally distributed, with a mean of 64.8 inches. Assume ó=2.8 inches. Are you more likely to randomly select 1 woman with a height less than 66.4 inches or are you more likely to select a sample of 26 women with a mean height less than 66.4 inches? Explain.

What is the probability of randomly selecting 1 woman with a height less than 66.4 inches?

Answer 1

µ = 64.8, σ = 2.8, n = 26

Probability of randomly selecting 1 woman with a height less than 66.4 inches, P(X < 66.4) =
= P( (X-µ)/σ < (66.4-64.8)/2.8 )
= P(z < 0.5714)
Using excel function:
= NORM.S.DIST(0.5714, 1)
= 0.7161

Probability to select a sample of 26 women with a mean height less than 66.4 inches, P(X̅ < 66.4) =
= P( (X̅-μ)/(σ/√n) < (66.4-64.8)/(2.8/√26) )
= P(z < 2.9137)
Using excel function:
= NORM.S.DIST(2.9137, 1)
= 0.9982

We are more likely to select a sample of 26 women.