Walter White is the founder and CEO of a B2C chemical manufacturing and distribution company located in the southwestern United States. Although business has been brisk in recent years, Walter's profits have been strained?like those of many small businesses?by the increasing cost of providing quality health care to his employees.

For questions a and b, suppose that the population of annual health care claims by employees is normally distributed with a mean of $9,500 and a standard deviation of $3,000.

1. What is the probability that an employee selected at random has health care claims exceeding $11,000?
2. Suppose that five employees are selected at random. What is the probability that the average health care claims of these five employees exceed $11,000?
3. Suppose that five employees are selected at random. What is the probability that all five of their health care claims each exceeds $11,000?
4. Suppose that Walter does not know the population mean of annual health care expenses, but he is willing to assume that the population standard deviation is $3,000. How many annual employee expenses does he need to sample to obtain a 95 percent confidence interval no larger than "plus or minus $500"?
5. Walter believes that the average annual health care claims per employee are less than $10,000, and he wants to find out if the data provide compelling evidence to support his claim. Write down the formal null and alternative hypotheses for the test Walter should perform. Do NOT perform the test.

To help him prepare for the meeting, Walter gathered the health insurance claims from the past year for a random sample of 36 of his employees. He entered the total claims for each employee in Excel and ran Descriptive Statistics. The output appears below. For the purpose of questions f and g, ignore the previous assumptions about mean and standard deviation.

EMPLOYEE CLAIMS 1 5 20,250 2 5 3,511] CLAIMS 3 5 12,000 Mean 9,600 4 5 13,375 Standard Error 800 5 5 8,450 Median 9,335 6 5 10,020 Mod e 10,020 7 5 14,550 Standard Deviation 4,801 8 5 9,775 Sample Variance 23,050,445 9 5 6,590 Kurtosis -0. 151 10 5 9,170 Skewness 0.118 11 5 12,120 Range 19,900 12 5 12,870 Mini mu m 350 13 5 5,000 Maximum 20,250 Sum 345,605 35 5 1,390 Count 36 36 5 10,020 \f\f