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Overdue Bills Following a Normal Curve & Determining Likely Voters

6. A large population of overdue bills has balances that follow a normal curve. When we take a sample of 100 of these the average is $500 and the SD is $100.
(a) What statement can you make about the range $300 to $700?
(b) What statement can you make about the range $480 to $520?

10. Pollsters try to determine whether or not a person is a 'likely voter' before they count their opinion in a poll. If we assume 40% of the registered voters will actually vote, in a random sample of 100 registered voters we can be 95% confident that somewhere between ________ and ________ of them will actually vote. Fill in the blanks with a number.

Please show your work so I can see what you did and help me better understand.

Solution Preview

a) Based on the Rule of Thumb (alternatively known as the 68-95-99.7 rule), we know that 95% of the values lie between +/- 2 standard deviations of the mean for a normal distribution. Since our standard deviation is $100 and our mean is $500, +/- 2 standard deviations translates to the exact range we are asked about. We can thus say that on average, we would expect 95 ...

Solution Summary

The solution is 261 words of explained calculations on how to answer these normal curve and range questions.