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The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year....

The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 50 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.3 pounds, what is the probability that the sample mean will be each of the following? Appendix A Statistical Tables

a. More than 60 pounds

d. Less than 55 pounds

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Expert Solution

We have given a random sample of households aluminum usage is monitored which is large , by the central limit theorem, the random variable has an approximately normal distribution.

The population mean with population standard deviation .

Now using as the Z-score for a given value.

(a) Probability that sample mean is more than 60 pounds.

So, the probability that the sample mean be more than 60 pounds is calculated as

________________

(b) Probability that sample mean be less than 55 pounds

So the probability that the sample mean be less than 55 pounds is calculated as

orchestra answered 3 years ago
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