Question

The height of women ages​ 20-29 is normally​ distributed, with a mean of 64.7 inches. Assume sigma equals 2.7 inches. Are you more likely to randomly select 1 woman with a height less than 66 inches or are you more likely to select a sample of 30 women with a mean height less than 66 ​inches? Explain.

What is the probability of randomly selecting 1 woman with a height less than 66 ​inches?

What is the probability of selecting a sample of 30 women with a mean height less than 66 inches?

Are you more likely to randomly select 1 woman with a height less than 66 inches or are you more likely to select a sample of 30 women with a mean height less than 66 inches? Choose the correct answer below.

A- It is more likely to select 1 woman with a height less than 66 inches because the probability is higher.

B- It is more likely to select 1 woman with a height less than 66 inches because the probability is lower

C- It is more likely to select a sample of 30 women with a mean height less than 66 inches because the sample of 30 has a higher probability

D- It is more likely to select a sample of 30 women with a mean height less than 66 inches because the sample of 30 has a lower probability.

Answer 1

Solution :

Given that ,

mean = = 64.7

standard deviation = = 2.7

a) P(x < 66 ) = P[(x - ) / < (66 - 64.7) /2.7 ]

= P(z < 0.48)

= 0.6844

probability = 0.6844

b) n = 30

= = 64.7

= / n = 2.7 / 30 = 0.4930

P( < 66 ) = P(( - ) / < (66 -64.7) /0.4930 )

= P(z < 2.64)

= 0.9959

probability = 0.9959

B- It is more likely to select 1 woman with a height less than 66 inches because the probability is lower