Question 1

The amount of a soft drink that goes into a typical 12-ounce bottle varies from bottle to bottle. It is normally distributed with mean12.03 ounces and 0.05 ounce.

1.If regulations require that bottles have at least 12 ounces of soda. What is the fraction of bottles that will contain at least 12 ounces of soda?

2.What is the fraction of bottles that will contain between 12 and 12.08 ounces of soda?

3.One percent of all bottles will contain more than what value?

4.Ten percent of all bottles will contain less than what value?

5.Every day, the company produces 10,000 bottles. The government inspect 10 randomly chosen bottles each day. If at least two are underfilled, the company is fined $10,000. What is the probability that the company will be fined on a given day?

Question 2

The amount of a soft drink that goes into a typical 12- ounce bottle varies from bottle to bottle. It is normally distributed with an adjustable mean and a fixed standard deviation of 0.05 ounce. (The adjustment is made to the filing machine).

1.If regulations require that bottles have at least 11.9 ounces, what is the smallest mean that can be used so that at least 99.5% of all bottles meet the regulation?

2.If the mean setting from part (a) is used, what is the probability that a typical bottle has at least 12 ounces?

Question 3

Problem to test for normality using Q-Q plot in R.

The fileCDRate.xlsxcontains the yields for a one-year certificate of deposit (CD) and a five-year CD for a sample of banks in the United States. For each type of investment (one-year or five-year CD), decide whether the data appear to be approximately normally distributed by constructing a Q-Q plot using R.

1.Provide the line of code to construct the Q-Q plot using R.

2.Paste the Q-Q plot for each type of investment.

3.Comment whether the data appear to be approximately normally distributed.

Question 4

Customers arrive at the drive-up window of a fast-food restaurant at a rate of 2 per minute during the lunch hour. (Exponential probability distribution.)

1.What is the probability that the next customer will arrive within 1 minute?

2.What is the probability that the next customer will arrive within 5 minutes?

3.During the dinner time period, the arrival rate is 1 per minute. What are your answers to (a) and (b) for this period?

Below is the data

Bank One-Year Five-Year Ally 1.04 1.98 Alostar Bank of Commerce 1.09 1.73 Bank of Internet USA 0.55 1.34 Barclays 0.80 2.22 Chartway Federal Credit Union 1.30 1.85 Colorado Federal 1.34 1.49 Discover 0.95 2.08 EH National 0.90 1.45 E-Loan 0.85 1.50 Ever 0.75 1.83 Fidelity 0.40 1.49 First Internet Bank of Indiana 1.00 2.10 FiveStar 0.40 1.39 Giantbank.com 1.00 1.60 Goldwater 0.95 1.20 Home Savings 1.19 2.13 Heritage Bank 0.23 0.93 Lone Star 0.70 1.75 New Dominion 0.59 0.49 Pentagon Federal Credit Union 1.00 1.60 Salem Five 0.80 1.98 Sychrony 1.22 2.23 TAB Bank 0.65 1.75 USAA 0.71 1.05 VirtualBank 1.15 1.80