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# To satisfy concerns of potential customers, the management of OurCampus! has undertaken a research project to learn the amount of time it takes...

1. To satisfy concerns of potential customers, the management of OurCampus! has undertaken a research project to learn the amount of time it takes users to load a complex video features page. The research team has collected data and has made some claims based on the assertion that the data follow a normal distribution. Open, which documents the work of a quality response team at OurCampus! Read the internal report that documents the work of the team and their conclusions. Then answer the following:

a. Can the collected data be approximated by the normal distribution?

b. Review and evaluate the conclusions made by the OurCampus! research team. Which conclusions are correct? Which ones are incorrect?

c. If OurCampus! could improve the mean time by five seconds, how would the probabilities change?

2. Toss a coin 10 times and record the number of heads. If each student performs this experiment five times, a frequency distribution of the number of heads can be developed from the results of the entire class. Does this distribution seem to approximate the normal distribution?

3. The advocacy group Consumers Concerned About Cereal Cheaters (CCACC) suspects that cereal companies, including Oxford Cereals, are cheating consumers by packaging cereals at less than labeled weights. Recently, the group investigated the package weights of two popular Oxford brand cereals. Open CCACC.pdf to examine the group's claims and supporting data, and then answer the following questions:

a. Are the data collection procedures that the CCACC uses to form its conclusions flawed? What procedures could the group follow to make its analysis more rigorous?

b. Assume that the two samples of five cereal boxes (one sample for each of two cereal varieties) listed on the CCACC website were collected randomly by organization members. For each sample, do the following:

i. Calculate the sample mean.

ii. Assume that the standard deviation of the process is 15 grams and the population mean is 368 grams. Calculate the percentage of all samples for each process that have a sample mean less than the value you calculated in (i).

iii. Again, assuming that the standard deviation is 15 grams, calculate the percentage of individual boxes of cereal that have a weight less than the value you calculated in (i).

c. What, if any, conclusions can you form by using your calculations about the filling processes for the two different cereals?

d. A representative from Oxford Cereals has asked that the CCACC take down its page discussing shortages in Oxford Cereals boxes. Is that request reasonable? Why or why not?

e. Can the techniques discussed in this chapter be used to prove cheating in the manner alleged by the CCACC? Why or why not?

4. Using Random Number Table E.1 from Page 544 of the textbook, simulate the selection of different-colored balls from a bowl, as follows:

a. Start in the row corresponding to the day of the month in which you were born.

b. Select one-digit numbers.

c. If a random digit between 0 and 6 is selected, consider the ball white; if a random digit is a 7, 8, or 9, consider the ball red.

Select samples of digits. In each sample, count the number of white balls and compute the proportion of white balls in the sample. If each student in the class selects five different samples for each sample size, a frequency distribution of the proportion of white balls (for each sample size) can be developed from the results of the entire class. What conclusions can you reach about the sampling distribution of the proportion as the sample size is increased?

Suppose that step c of this problem uses the following rule: "If a random digit between 0 and 8 is selected, consider the ball to be white; if a random digit of 9 is selected, consider the ball to be red." Compare and contrast the results in this problem and those in step c.

5. The fill amount of bottles of a soft drink is normally distributed, with a mean of 2.0 liters and a standard deviation of 0.05 liter. If you select a random sample of 25 bottles, what is the probability that the sample mean will be

a. between 1.99 and 2.0 liters?

b. below 1.98 liters?

c. greater than 2.01 liters?

d. The probability is 99% that the sample mean amount of soft drink will be at least how much?

e. The probability is 99% that the sample mean amount of soft drink will be between which two values (symmetrically distributed around the mean)?