Question

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

64.7

inches. Assume

sigmaσequals=2.7

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

67.267.2

inches or are you more likely to select a sample of

10

women with a mean height less than

67.2

​inches? Explain.

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

67.2

​inches?

nothing

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

Answer 1

It is given that

Population mean

Population standard deviation

We have to find the probability for a randomly selected woman with a height less than 67.2 inches, i.e. x = 67.2

Using the formula

setting the given values, we get

this gives us

using z distribution table for the value 0.9259,(look for 0.9 in the left most column and 0.03 in the top most row, then select the intersecting cell) , we get  

Probability = 0.8238

Population mean

Population standard deviation

sample size = 10

We have to find the probability for a sample mean of 10 woman with a height less than 67.2 inches, i.e. x(bar) = 67.2

Using the formula

setting the given values, we get

this gives us

using z distribution table for the value 2.928(look for 2.9 in the left most column and 0.03 in the top most row, then select the intersecting cell) , we get

Probability = 0.9983

So, we are more likely to select a sample of 10 women with a mean height less than 67.2 inches because it has higher probability.