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In: Statistics and Probability

A survey found that the American family generates an average of 17.2 pounds of glass garbage...

A survey found that the American family generates an average of 17.2 pounds of glass garbage each year. Assume the standard deviation of the distribution is 2.5 pounds Find the probability that the mean of a sample of 35 families will be between 16.9 and 17.9 pounds. Assume that the sample is taken from a large population and the correction factor can be ignored. Round your final answer to four decimal places and intermediate -value calculations to two decimal places.

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Expert Solution

We are given that the population mean and the standard deviation . We also know that the sample mean then also follow a Normal distribution with mean and standard deviation .

Hence the  probability that the mean of a sample of 35 families will be between 16.9 and 17.9 pounds is

. Since follows a Normal distribution, we can transform to

to a standard Normal distribution. In our problem, n=35 and when ,

when

,

  

These probabilities will be calculated using NORM.S.DIST(-0.7099,true) function in EXCEL.

orchestra answered 2 years ago
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