The school board of For sight County considers its most important task to be keeping the average class size in For sight County schools less than the average class size in neighboring Hindsight County. Miss Dee Marks, the school superintendent for For sight County, has just received reliable information indicating that the average class size in Hindsight County this year is 30.3 students. She does not yet have the figures for all 621 classes in her own school system, so Dee is forced to rely upon the 76 classes that have reported class sizes, yielding an average class size of 29.8 students. Dee knows that the class size of For sight County classes has a distribution with an unknown mean and standard deviation equal to 8.3 students. Assuming that the sample of 76 that Miss Marks possesses is randomly chosen from the population of all For sight County class sizes:
- Find an interval that Dee can be 95.5 percent certain will contain the true mean.
- Do you think that Dee has met her goal?
- If the price per kwh is $0.12, within what interval can Gwen be 68.3 percent certain that the average August cost for electricity will lie?
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