Question

The height of women ages​ 20-29 is normally​ distributed, with a mean of 64.2 inches. Assume sigmaequals2.9 inches. Are you more likely to randomly select 1 woman with a height less than 65.3 inches or are you more likely to select a sample of 29 women with a mean height less than 65.3 ​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 65.3 ​inches?

Answer 1

a)

Let X represent the height of a woman.

Then X ~ Normal(64.2 , 2.9²)

The following information has been provided:

We need to compute . The corresponding z-value needed to be computed:

Therefore,

Hence the probability of selecting a woman with height less than 65.3 inches is 64.78%

The following is obtained graphically:

b)

Now

i.e.

The following information has been provided:

We need to compute . The corresponding z-value needed to be computed:

Therefore,

The following is obtained graphically:

More likely to select the second sample.

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