Assignment

All assignments should be written in your own words providing examples and opinions beyond the textbook or any other source. For calculations show ALL your steps included calculator/Excel keystrokes and/or formulas. If you find it easier you can always attach an excel spreadsheet which would include formulas in the cells so you don’t have to rewrite. I will be looking at showing your explanation of your results for full credit, do not just provide a number answer without explaining it.

Chapter 6
1. Suppose that the times required for a company to fix cable problems in the homes of its customers are uniformly distributed between 40 minutes and 65 minutes. What is the probability that a randomly selected cable repair visit falls within 2 standard deviations of the mean?

2. An apple juice producer buys all his apples from a conglomerate of apple growers in one state. The amount of juice squeezed from each of these apples is approximately normally distributed with a mean of 2.25 ounces and a standard deviation of 0.15 ounce. What is the probability that a randomly selected apple will contain between 2.00 and 2.50 ounces? Briefly Discuss.

3. A major card company has determined that its customers charge an average of $280 per month on their accounts with a standard deviation of $20.
a. What percentage of the customers charges more than $275 per month?
b. What percentage of the customers charges less than $243 per month?
c. What percentage of the customers charges between $241 and $301.60 per month?

4. In a normal distribution, it is known that 27.34% of all the items are included from 100 up to the mean, and another 45.99% of all the items are included from the mean up to 145. Determine the mean and the standard deviation of the distribution.
What do these numbers tell us?

Chapter 8
5. At the end of 2010, 2011, and 2012, the average prices of a share of stock in a portfolio were $34.83, $34.65, and $31.26 respectively. To investigate the average share price at the end of 1993, a random sample of 30 stocks was drawn and their closing prices on the last trading day of 2013 were observed with a mean of 33.583 and a standard deviation of 19.149. Estimate the average price of a share of stock in the portfolio at the end of 2013 with a 90 percent confidence interval. Briefly discuss.

6. Health insurers and the federal government are both putting pressure on hospitals to shorten the average length of stay (LOS) of their patients. In 2016, the average LOS for non-heart patients was 4.6 days. A random sample of 20 hospitals in one state had a mean LOS for non-heart patients in 2000 of 3.8 days and a standard deviation of 1.2 days. Calculate a 95 percent confidence interval for the population mean LOS for non-heart patients in these hospitals in 2016. Briefly discuss.

7. An auditor is interested in estimating the mean outstanding defaulted loans balance of all defaulted loans over the last three years. A random sample of 20 defaulted loans yielded a mean of $67,918 with a standard deviation of $16,552.40. Calculate a 90 percent confidence interval for the mean balance of defaulted loans over the past three years. Briefly discuss.

8. In a campaign to eliminate non-returnable containers, a poll of 600 voters showed 210 of them opposed the container control bill. Develop a 92% confidence interval estimate for the proportion of all the voters who opposed this bill. What does this interval tell us?

9. A local health center noted that in a sample of 400 patients, 80 were referred to
them by the local hospital.
a.Provide a 95% confidence interval for all the patients who are referred to the health center by the hospital.
b. What sample size would be required to estimate the proportion of all hospital referrals to the health center with a margin of error of .04 or less at 95% confidence? What does this represent?

Assignment All assignments should be written in your own words...