The mean height of women in a country​ (ages 20 −​29) is 63.9 inches. A random sample of 55 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64 inches? Assume σ= 25.2 . The probability that the mean height for the sample is greater than 64 inches is________ (Round to four decimal places as​ needed.)

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Asked Mar 5, 2019

The mean height of women in a country (ages 20 29) is 63.9 inches. A random sample of 55 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64 inches? Assume σ= 25.2 . 

The probability that the mean height for the sample is greater than 64 inches is________ (Round to four decimal places as needed.) 

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Step 1

Introduction:

A random sample of size n = 55 women in the age of 20-29 years is selected.

Let X denotes the height of a randomly selected women.

Denote the population mean, that is, the mean height of all the women in the age of 20-29 years as μ and the standard deviation in height of all the women in the age of 20-29 years as σ.

Here, μ =63.9 inches and σ = 25.2 inch.

Denote the sample mean height of 55 randomly selected women as X-bar.

Step 2

Sampling distribution of sample mean:

The sample mean of a random variable X has a sampling distribution that has population mean or expected value same as that of X and population standard deviation, called the standard error, which is the population standard deviation of X divided by the square root of the sample size n. The parameters are as follows:

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Step 3

Central limit theorem:

If X1, X2, …, Xn are independent and identically distributed (iid) random variables with finite mean, E(Xi) = μ and finite variance V(Xi) = σ2, then Z will converge to ...

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