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Statistics: Mean, the Variance, and the Standard Deviation

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Determine the mean, the variance, and the standard deviation of the following discrete
distribution.
x P(x)
0 .103
1 .118
2 .246
3 .229
4 .138
5 .094
6 .071
7 .001

According to a recent survey, the probability that a passenger files a complaint with the Department of Transportation about a particular U.S. airline is .000014. Suppose 100,000 passengers who flew with this particular airline are randomly contacted.

a. What is the probability that exactly five passengers filed complaints?

b. What is the probability that none of the passengers filed complaints?

c. What is the probability that more than six passengers filed complaints?

A Department of Transportation survey showed that 60% of U.S. residents over 65 years of age oppose use of cell phones in flight even if there were no issues with the phones interfering with aircraft communications systems. If this information is correct and if a researcher randomly selects 25 U.S. residents who are over 65 years of age,

a. What is the probability that exactly 12 oppose the use of cell phones in flight?

b. What is the probability that more than 17 oppose the use of cell phones in flight?

c. What is the probability that less than eight oppose the use of cell phones in flight? If the researcher actually got less than eight, what might she conclude about the Department of Transportation survey?

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The solution determines the mean, the variance, and the standard deviation.

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