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# Probability, Samples, Confidence Intervals

5.6 A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail. (c) One or the other will fail. Show your steps carefully.

5.7The probability is 1 in 4,000,000 that has a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes 50,000 trips. (a) What is the probability of the fatal accident over a lifetime? Explain your reasoning carefully. Hint Assume independence be violated? (b) Why might a driver be tempted not to use a seat belt "just on this trip?

8.4 A random sample of 10 miniature tootsie rolls was taken from a bag. Each piece was weighed on a very accurate scale. The results in grams were:

3.087, 3.131, 3.241, 3.241, 3.270, 3.353, 3.400, 3.411, 3.437, 3.477
(A) Construct a 90 percent confidence interval for the true mean weight. (b) What sample size would be necessary to estimate the true weight with an error of 0.03 grams with 90 percent confidence? (c) Discuss the factors, which might cause variation in the weight of tootsie rolls during manufacture. (Data are fro project by MBA student Henry Scussel). Tootsie

8.6 In 1992, the FAA conducted 86,991 pre employment drug tests on the job applicants who were to engaged in safety related jobs and found that 1143 were positive. (A) Construct 95 percent confidence intervals for the population proportion of positive drug test. (b) Why is the normality assumption not a problem, despite the very small value of p? (Data from flying 120 no 11 (November 1993 pg 31.) Are ethics and legal restrictions the same?

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5.6 A certain airplane has two independent alternators to provide electrical power. The probability that a given alternator will fail on a 1-hour flight is .02. What is the probability that (a) both will fail? (b) Neither will fail. (c) One or the other will fail. Show your steps carefully.
Solution:
(a) both will fail?

The probability that both will fail= probability that 1st one will fail* probability that 2nd one will fail
Because both alternators are independent.

The probability that both will fail=.02*.02=0.0004

(b) Neither will fail?

The probability that both neither will fail=0.98*.98=0.9604
(c) One or the other will fail? Show all steps carefully.

The probability that One or the other will fail = probability that 1st one will fail* probability that 2nd one will not fail + probability that 1st one will not fail* probability that 2nd one will fail=0.02*.98+.98*.02= 0.0392

5.7The probability is 1 in 4,000,000 that has a single auto trip in the United States will result in a fatality. Over a lifetime, an average U.S. driver takes ...

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Solutions to given questions.

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