Question

The height of women ages​ 20-29 is normally​ distributed, with a mean of 64.5 inches. Assume σ=2.4 inches. Are you more likely to randomly select 1 woman with a height less than 66.2 inches or are you more likely to select a sample of 21 women with a mean height less than 66.2 ​inches? Explain.

What is the probability of randomly selecting 1 woman with a height less than 66.2 ​inches ​(Round to four decimal places as​ needed.)

What is the probability of selecting a sample of 21 women with a mean height less than 66.2 ​inches? ​(Round to four decimal places as​ needed.)

Are you more likely to randomly select 1 woman with a height less than 66.2 inches or are you more likely to select a sample of 21 women with a mean height less than 66.2 ​inches? Choose the correct answer below.

A.It is more likely to select a sample of 21 women with a mean height less than 66.2 inches because the sample of 21 has a lower probability.

B.It is more likely to select a sample of 21 women with a mean height less than 66.2 inches because the sample of 21 has a higher probability.

C.It is more likely to select 1 woman with a height less than 66.2 inches because the probability is lower.

D.It is more likely to select 1 woman with a height less than 66.2 inches because the probability is higher.

Answer 1

Let x: height of women

x follows normal distribution with mean =64.5 and standard deviation 2.4

convert the x score to z score and find the probability

answer with steps given below