Three different beverages are sold at a fast food restaurant soft drinks, tea, and coffee.

a. Explain why the type of beverage sold is an example of a categorical variable.

b. Explain why the type of beverage sold is an example of a nominal scaled variable.

c. Soft drinks are sold in three sizes at a fast-food restaurant small, medium, and large. Explain why the size of the soft drink is an example of an ordinal scaled variable.

2.Suppose that you measure the time it takes to download an MP3 file from the Internet.

a. Explain why the download time is a continuous numerical variable.

b. Explain why the download time is a ratio scaled variable

3.A manufacturer of cat food was planning to survey households in the United States to determine purchasing habits of cat owners. Among the questions to be included are those that relate to 1. where cat food is primarily purchased. 2. whether dry or moist cat food is purchased. 3. the number of cats living in the household. 4. whether the cat is pedigreed.

a. Describe the population.

b. For each of the four items listed, indicate whether the variable is categorical or numerical. If it is numerical, is it discrete or continuous?

c. Develop five categorical questions for the survey.

d. Develop five numerical questions for the survey

4.One of the major measures of the quality of service provided by any organization is the speed with which the organization responds to customer complaints. A large family-held department store selling furniture and flooring, including carpet, had undergone a major expansion in the past several years. In particular, the flooring department had expanded from 2 installation crews to an installation supervisor, a measurer, and 15 installation crews. During a recent year, the company got 50 complaints concerning carpet installation.

The following data represent the number of days between the receipt of the complaint and the resolution of the complaint:

54535137312715221238174271119126110110296135943126512

41653229282926251141313105274523022362620233368

a. Construct a frequency distribution and a percentage distribution.

b. Construct a histogram and a percentage polygon.

c. Form a cumulative percentage distribution and plot a cumulative percentage polygon (ogive).

d. On the basis of the results of (a) through (c), if you had to tell the president of the company how long a customer should expect to wait to have a complaint resolved, what would you say? Explain.

5.In New York State, savings banks are permitted to sell a form of life insurance called savings bank life insurance (SBLI). The approval process consists of underwriting, which includes a review of the application, a medical information bureau check, possible requests for additional medical information and medical exams, and a policy compilation stage during which the policy pages are generated and sent to the bank for delivery. The ability to deliver approved policies to customers in a timely manner is critical to the profitability of this service to the bank. During a period of one month, a random sample of 27 approved policies was selected, and the following total processing times in days, were recorded:

731916642828319060563156221845481717179192635051691617

a. Compute the mean, median, first quartile, and third quartile.

b. Compute the range, interquartile range, variance, standard deviation, and coefficient of variation.

c. Construct a box-and-whisker plot. Are the data skewed? If so, how? d. What would you tell a customer who enters the bank to purchase this type of insurance policy and asks how long the approval process takes?

6.A soft drink bottling company maintains records concerning the number of unacceptable bottles of soft drink from the filling and capping machines. Based on past data, the probability that a bottle came from machine I and was nonconforming is 0.01, and the probability that a bottle came from machine II and was nonconforming is 0.005. Half the bottles are filled on machine I. The other half are filled on machine II.

If a filled bottle of soft drink is randomly selected, what is the probability that

a. it is a nonconforming bottle?

b. it was filled on machine I and is a conforming bottle?

c. it was filled on machine I or is a conforming bottle?

d. Suppose you know that the bottle was filled on machine I. What is the probability that it is nonconforming?

e. Suppose you know that the bottle is nonconforming. What is the probability that it was filled on machine I?

f. Explain the difference in the answers to (d) and (e). (Hint: Construct a 2 * 2 contingency table to evaluate the probabilities.)

7. The fill amount in 2 liter soft drink bottles is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.05 liter. If bottles contain less than 95% of the listed net content (1.90 liters, in this case), the manufacturer may be subject to penalty by the state office of consumer affairs. Bottles that have a net content above 2.10 liters may cause excess spillage upon opening. What proportion of the bottles will contain:

a. between 1.90 and 2.0 liters?

b. between 1.90 and 2.10 liters?

c. below 1.90 liters or above 2.10 liters?

d. At least how much soft drink is contained in 99% of the bottles?

e. ninety-nine percent of the bottles contain an amount that is between which two values (symmetrically distributed) around the mean?

8. The major stock market indexes had strong results in 2014. The mean one year return for stocks in the S&P 500 a group of 500 very large companies, was + 11.4%. The mean one year return for the NASDAQ , a group of 3,200 small andsized companies was + 13.4% . Historically the one year returns are approximately normally distributed, the standard deviation in the S&P 500 is approximately 20% and the standard deviation in the NASDAQ is approximately 30%.

a. what is the probability that a stock in the S&P 500 gained value in 2014?

b. what is the probability that a stock in the S&P 500 gained 10% or more in 2014?

c. what is the probability that a stock in the S&P 500 lost 20% or more in 2014?

d. what is the probability that a stock in the S&P 500 lost 30% or more in 2014?

e. What is the probability that a stock in the NASDAQ gained value in 2014?

f. what is the probability that a stock in the NASDAQ gained 10% or more in 2014?

g. What is the probability that a stock in the NASDAQ lost 20% or more in 2014?

h. what is the probability that a stock in the NASDAQ lost 30% or more in 2014?

i. submit a short summary on your findings. Be sure to include a discussion of the risk associated with a large standard deviation.