According to the Gallup Poll, $27\%$ of U.S. adults have high levels of cholesterol. Gallup reports that such elevated levels "could be financially devastating to the U.S. healthcare system" and are a major concern to health insurance providers. According to recent analyses, cholesterol levels in healthy U.S. adults average about $215 \mathrm{mg} / \mathrm{dL}$ with a standard deviation of about $30 \mathrm{mg} / \mathrm{dL}$ and are roughly Normally distributed. If the cholesterol levels of a sample of 42 healthy U.S. adults are taken, what is the probability that the mean cholesterol level of the sample:

a) Will be no more than 215?

According to the Gallup Poll, $27\%$ of U.S. adults have high levels of cholesterol. Gallup reports that such elevated levels "could be financially devastating to the U.S. healthcare system" and are a major concern to health insurance providers. According to recent analyses, cholesterol levels in healthy U.S. adults average about $215 \mathrm{mg} / \mathrm{dL}$ with a standard deviation of about $30 \mathrm{mg} / \mathrm{dL}$ and are roughly Normally distributed. If the cholesterol levels of a sample of 42 healthy U.S. adults are taken, what is the probability that the mean cholesterol level of the sample:

c) Will be less than 200?

In a really large bag of M&M's, we found $12\%$ of $500$ candies were green. Is this proof that the manufacturing process is out of control and has made too many greens? Describe.

For a sample of 36 houses, what would you wish the distribution of the sale prices to be? A real estate agent has been assigned 10 houses at random to sell this month. She wants to know whether the mean price of those houses is typical. What, if anything, does she need to assume about the distribution of prices to be able to use the Central Limit Theorem? Are those assumptions valid?

Suppose that a variable of a population has a bell-shaped distribution. If you take a large simple random sample from the population, roughly what shape would you expect the distribution of the sample to be? Explain your answer.

The mayor of a small city has suggested that the state locate a new prison there, arguing that the construction project and resulting jobs will be good for the local economy. A total of 183 residents show up for a public hearing on the proposal, and a show of hands finds only 31 in favor of the prison project. What can the city council conclude about public support for the mayor’s initiative?

The mayor of a small city has suggested that the state locate a new prison there, arguing that the construction project and resulting jobs will be good for the local economy. A total of 183 residents show up for a public hearing on the proposal, and a show of hands finds only 31 in favor of the prison project. What can the city council conclude about public support for the mayor's initiative?

In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." As a lesson, the professor has selected pages of the Journal for which exactly half the publicly traded stocks went up and half went down. He watches a cable news show about investing and during the show throws his darts at the pages of the Journal. He claims that of 200 stocks picked in this manner, $58 \%$ were winners.

b) If there are 100 students in the class, are you surprised that one was this successful? Explain.

In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." As a lesson, the professor has selected pages of the Journal for which exactly half the publicly traded stocks went up and half went down. He watches a cable news show about investing and during the show throws his darts at the pages of the Journal. He claims that of 200 stocks picked in this manner, $58 \%$ were winners.

a) What do you think of his claim? Explain.

Listed below are measured amounts of caffeine (mg per 12oz of drink) obtained in one can from each of 20 brands (7-UP, A&W Root Beer, Cherry Coke, ... , Tab). Are the statistics representative of the population of all cans of the same 20 brands consumed by Americans?

$$\begin{matrix} \text{0} & \text{0} & \text{34} & \text{34} & \text{34} & \text{45} & \text{41} & \text{51} & \text{55} & \text{36} & \text{47} & \text{41} & \text{0} & \text{0} & \text{53} & \text{54} & \text{38} & \text{0} & \text{41} & \text{47}\\ \end{matrix}$$

In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." As a lesson, the professor has selected pages of the Journal for which exactly half the publicly traded stocks went up and half went down. The professor then makes a histogram of the reported proportions.

b) Where do you wish the histogram to be centered?

In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." As a lesson, the professor has selected pages of the Journal for which exactly half the publicly traded stocks went up and half went down. The professor then makes a histogram of the reported proportions.

d) Describe why a Normal model should not be used here.

In a large Business Statistics class, the professor has each person select stocks by throwing 16 darts at pages of the Wall Street Journal. They then check to see whether their stock picks rose or fell the next day and report their proportion of "successes." As a lesson, the professor has selected pages of the Journal for which exactly half the publicly traded stocks went up and half went down. The professor then makes a histogram of the reported proportions.

b) Confirm that you can use a Normal model here.

From a survey of coworkers, you find that $48 \%$ of 200 have already received this year's flu vaccine. An approximate $95 \%$ confidence interval is $(0.409,0.551)$. Is the following true? If not, describe briefly.

e) We are $95 \%$ confident that between $40.9 \%$ and $55.1 \%$ of the samples will have a proportion near $48 \%$.