Question

The height of women ages​ 20-29 is normally​ distributed, with a mean of

63.5inches. Assume sigma σequals=2.4inches. Are you more likely to randomly select 1 woman with a height less than 65.1inches or are you more likely to select a sample of 23women with a mean height less than 65.1inches?

Please answer :

1-What is the probability of randomly selecting 1 woman with a height less than

65.1inches?

​(Round to four decimal places as​ needed.)

2-What is the probability of selecting a sample of

23women with a mean height less than 65.1inches?

​(Round to four decimal places as​ needed.)

Are you more likely to randomly select 1 woman with a height less than

65.1

inches or are you more likely to select a sample of

23

women with a mean height less than

65.1

​inches? Choose the correct answer below.

A.

It is more likely to select 1 woman with a height less than

65.1

inches because the probability is lower.

B.

It is more likely to select 1 woman with a height less than

65.1

inches because the probability is higher.

C.

It is more likely to select a sample of

23

women with a mean height less than

65.1

inches because the sample of

23

has a lower probability.

D.

It is more likely to select a sample of

23

women with a mean height less than

65.1

inches because the sample of

23

has a higher probability.

Answer 1

Solution:-

Mean = 63.50, S.D = 2.4

1) The probability of randomly selecting 1 woman with a height less than 65.1 inches is 0.7475

x = 65.1

By applying normal distribution:-

z = 0.6667

P(z < 0.6667) = 0.7475

2) The probability of selecting a sample of 23 women with a mean height less than 65.1 inches is 0.9993.

x = 65.1

By applying normal distribution:-

z = 3.197

P(z < 3.197) = 0.9993

D) It is more likely to select a sample of 23 women with a mean height less than 65.1 inches because the sample of 23 has a higher probability.