Question

The height of women ages? 20-29 is normally? distributed, with a mean of 63.9 inches. Assume sigmaequals2.4 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 10 women with a mean height less than 66.2 ?inches? Explain. LOADING... Click the icon to view page 1 of the standard normal table. LOADING... Click the icon to view page 2 of the standard normal table. What is the probability of randomly selecting 1 woman with a height less than 66.2 ?inches? nothing ?(Round to four decimal places as? needed.) What is the probability of selecting a sample of 10 women with a mean height less than 66.2 ?inches? 1 ?(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 10 women with a mean height less than 66.2 ?inches? Choose the correct answer below. A. It is more likely to select 1 woman with a height less than 66.2 inches because the probability is lower. B. It is more likely to select a sample of 10 women with a mean height less than 66.2 inches because the sample of 10 has a lower probability. C. It is more likely to select 1 woman with a height less than 66.2 inches because the probability is higher. D. It is more likely to select a sample of 10 women with a mean height less than 66.2 inches because the sample of 10 has a higher probability. Click to select your answer(s).

Answer 1

Let X is a random variable shows the height of woman. Here X has normal distribution with following parameters

The z-score for X = 66.2 is

The probability that woman height is less than 66.2 inches is

The z-score for is

The probability that mean women height in sample of 10 is less than 66.2 inches is

?

D. It is more likely to select a sample of 10 women with a mean height less than 66.2 inches because the sample of 10 has a higher probability.