The idea of insurance is that we all face risks that are unlikely but carry high cost. Think of a fire destroying your home. So we form a group to share the risk: we all pay a small armount, and the insurance policy pays a large amount to those few of us whose homes burn down. An insurance company looks at the records for millions of homeowners and sees that the mean loss from fire in a year is μ $500 per house and that the standard deviation of the loss is σ $10,000. (The distribution of losses is extremely right-skewed: most people have $0 loss, but a few have large losses.) The company plans to sell fire insurance for $500 plus enough to cover its costs and profit.

(a) Explain clearly why it would be unwise to sell only 100 policies. Then explain why selling many thousands of such policies is a safe business

(b) Suppose the company sells the policies for $600. If the company sells 50,000 policies, what is the approximate probability that the average loss in a year will be greater than $600?

The hawthorne works was a large western electric factory with 45,000 employees. during the 1920s and 1930s, hawthorne works was the site of some well-known industrial studies. in one of the studies, researchers investigated the impact of different working conditions on worker productivity. prior to the start of the study, researchers secretly measured workers' productivity for several weeks. then researchers chose two workers, who then chose their own teams. the teams were separated from the general workforce and completed their work in different experiment rooms where the researchers could observe them more easily. over a 5-year period researchers manipulated the structure of the workday for each team (number and duration of breaks and number of hours per shift). for each of these changes in working conditions, the researchers measured the effect on productivity. for some conditions, such as frequent short breaks, workers rebelled by intentionally decreasing productivity.why did the researchers secretly measure the workers' productivity before creating the two treatment groups? a, to create similar treatment groups so that a cause-and-effect relationship could be establishedb, to draw conclusions about the productivity of all workers in the plant based on the test groupsc, to directly control for confounding variablesd, to provide a baseline for measuring worker productivity