According to the Current Population Reports published by the

According to the Current Population Reports, published by the U.S. Bureau of the census, the mean annual alimony income received by women is $4,000. Assume a standard deviation of $7,500. Suppose 100 women are selected at random. Determine the probability that the mean annual alimony received by the 100 woman is within $500 of the population mean (sentence). Is it necessary to assume that the population of annual alimony payments is normally distributed? Explain your answer. Determine the probability that the mean annual alimony received by the 1000 woman is within $500 of the population mean (sentence). For the alimony incomes considered here, why is it necessary to take such a large sample in order to be assured of a relatively small sampling error? Judy\'s doctor is concerned that she may suffer from hypokalemia (low potassium in the blood). There is variation both in the actual potassium level and in the blood test that measures the level. Judy\'s measured potassium level varies according to the normal distribution with mu = 3.8 and sigma = 0.2. A patient is classified as hypokalemic if the potassium level is below 3.5. If a single measurement is made, what is the probability that Judy is diagnosed as hypokalemic (Sentence)?

Solution

D)

Obviously, the incomes are not normally distributed, because the standard deviation is already larger than the mean.

Now, to use the normal distribution for the sample means, the central limit theorem needs a sufficiently large number of iterates, hence, a large enough sample size.