# Project #29805 - stats test 6

Test #6 - Sampling Distribution

Statistics

Tanaka

make sure to list the shape in each problem or you will lose  points open book and open note test

1. According to the U.S. Bureau of Labor Statistics, the mean weekly wage for manufacturing workers was \$517 in February 1996. Assume that the weekly wages for all manufacturing workers for February 1996 are normally distributed with a mean of \$517 and standard deviation of \$65. Find the probability that the mean weekly wage for a random sample of 25 manufacturing workers taken from this population would be

a. between \$527 and \$53 7

b. within \$ 15 of the population mean weekly wage

c. lower than the population mean by \$20 or more

2. The balances of all savings accounts at a local bank have a distribution that is skewed to the right with its mean equal to \$12,450 and standard deviation equal to \$4,160. Find the probability that the mean balance of a sample of 50 savings accounts selected from this bank will be

a. more than \$11,500

b. between \$12,000 and \$13,800

c. within \$ 1,500 of the population mean

d. more than the population mean by at least \$ 1,000

3. Seventy percent of adults favor some kind of government control on the prices of medicines. Assume that this percentage is true for the current population of all adults.

a. Find the probability that the proportion of adults in a random sample of 400 who favor some kind of government control on the prices of medicine is

i. less than .65

ii.   between .73 and .76

b. What is the probability that the proportion of adults in a random of 400 who favor some kind of government control is within .06 of the population proportion?

c. What is the probability that the sample proportion is greater than the population proportion by .05 or more?

4. According to a recent CNN poll, 62% of American adults are frighten always, most of the time, or sometimes when flying on small commuter airplanes. Assume that this result holds true for the current population of all American adults. Let p-hat be the proportion in a random sample of 100 adults who are frighten of flying on small commuter airplanes.

a. What is the probability that this sample proportion is within .08 of the population proportion?

b. What is the probability that this sample proportion is lower than the population proportion by .10 or more?

c. What is the probability that this sample proportion is greater than the population proportion by .09 or more?

5. In a clinical study, the average daily fat intake of U.S. adults with children in the household was 91.4 grams, with a standard deviation of 93.25 grams. These results were based on a sample of 3714 adults. Suppose that these results hold true for the current population distribution of daily fat intake of such adults, and that this distribution is strongly skewed to the right. Let x bar be the average daily fat intake of 20 randomly selected U.S. adults with children in the household. Find the mean and the standard deviation of the sampling distribution of x bar. Do the same for a random sample of size 75. How do the shapes of the sampling distributions differ for the two sample sizes?

 Subject Mathematics Due By (Pacific Time) 05/03/2014
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