Question

The height of women ages​ 20-29 are normally​ distributed, with a mean of 64.3 inches. Assume sigmaequals2.5 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 18 women with a mean height less than 66.2 ​inches? Explain. What is the probability of randomly selecting 1 woman with a height of less than 66.2 ​inches? _______​(Round to four decimal places as​ needed.) What is the probability of selecting a sample of 18 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 18 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 18 women with a mean height less than 66.2 inches because the sample of 18 has a lower probability.

C. It is more likely to select a sample of 18 women with a mean height less than 66.2 inches because the sample of 18 has a higher probability.

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

Answer 1

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 18 women with a mean height less than 66.2 ​inches? Choose the correct answer below.

Answer :- C. It is more likely to select a sample of 18 women with a mean height less than 66.2 inches because the sample of 18 has a higher probability.

The values provided in the above question are as below

Mean = = 64.3

Standard deviation = = 2.5

Step 1)

We find the probability of randomly selecting 1 woman with a height of less than 66.2 ​inches

---------(1)

We convert above into using following formula

----------(2)

Using equation (2) in equation (1) we get

We calculate the above probability using Standard normal table

The probability of randomly selecting 1 woman with a height of less than 66.2 ​inches is 0.7764

Now,

Step 2)

We find the probability of selecting a sample of 18 women with a mean height less than 66.2 ​inches

=

-------------(3)

We convert above into using following formula

----------------(4)

Using equation (4) in equation (3) we get

We calculate the above probability using following Excel function

=NORMSDIST(z)

Here, z = 3.224406922

=NORMSDIST(3.224406922) then press Enter we get probability as

= 0.999368831

The probability of selecting a sample of 18 women with a mean height less than 66.2 ​inches is 0.999368831

Or

We also calculate the above probability using Standard normal table

First we convert above into two decimal places as below

(Using Standard normal table)

The probability of selecting a sample of 18 women with a mean height less than 66.2 ​inches is 0.9994

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 18 women with a mean height less than 66.2 ​inches? Choose the correct answer below.

Answer :- C. It is more likely to select a sample of 18 women with a mean height less than 66.2 inches because the sample of 18 has a higher probability.

Summary :-

Step 1)

The probability of randomly selecting 1 woman with a height of less than 66.2 ​inches is 0.7764

Step 2)

1) Using Excel function

The probability of selecting a sample of 18 women with a mean height less than 66.2 ​inches is 0.999368831

2) Using Standard normal table

The probability of selecting a sample of 18 women with a mean height less than 66.2 ​inches is 0.9994

Choose the correct answer below.

C. It is more likely to select a sample of 18 women with a mean height less than 66.2 inches because the sample of 18 has a higher probability.