Posted by **lauren** on Saturday, February 16, 2008 at 5:10pm.

An important indicator of lung function is forced expiratory volume(FEV), which is the volume of air that a person can expire in one second. Dr. Jones plans to measure FEv in a random sample of n young women from a certain population, and to use the sample mean as an estimate of the population mean. Let E be the event that Jones's sample mean will be within +- 100mLi of the population mean.Assume that the population distribution is normal with mean 3000 mLi and standard deviation 400 mLi. Find Pr{E} if:

A)n=15

- statistics -
**Damon**, Saturday, February 16, 2008 at 6:55pm
mean of sample means = mean of population = 3000

sigma sample means = sigma population/sqrt n

so s sample mean = 400/sqrt(15)

= 103

100/103 = .971 s

so we are interested in between the mean -.971 sigma to the mean +.971 sigma

from tables of normal distribution you can get the probability of being beyond mean +.971 sigma

it is 1-.834 = .166

by symmetry the probability of being below mean -.971 sigma is also .166

so the probability of being above or below the desired range i 2*.166 = .332

so the probability of being within the desired range is

1-.332 = .668 or 67 %

This makes sense because we all know that about 68 % lies within 1 sigma and we are at almost 1 sigma, namely .971 sigma

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