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Chapter 5: Problem 47
In how many ways can a sample (without replacement) of 9 items be selected from a population of 20 items?
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Briefly explain the following. a. A binomial experiment b. A trial c. A binomial random variable
GESCO Insurance Company charges a \(\$ 350\) premium per annum for a \(\$ 100,000\) life insurance policy for a 40 -year-old female. The probability that a 40 -year-old female will die within 1 year is \(.002 .\) a. Let \(x\) be a random variable that denotes the gain of the company for next year from.a \(\$ 100,000\) life insurance policy sold to a 40 -year-old female. Write the probability distribution of \(x\) b. Find the mean and standard deviation of the probability distribution of part a. Give a brief interpretation of the value of the mean.
In a 2006 ABC News poll, \(37 \%\) of adult Americans stated that they encounter "rude and disrespectful behavior" often (Source: http://abcnews.go.com/images/Politics/1005alHowRude.pdf). Suppose that this result holds true for the current population of adult Americans. Suppose that two adult Americans are selected at random. Let \(x\) denote the number of adult Americans in these two who encounter "rude and disrespectful behavior" often. Construct the probability distribution table of \(x\). Draw a tree diagram for this problem.
Bender Electronics buys keyboards for its computers from another company. The keyboards are received in shipments of 100 boxes, each box containing 20 keyboards. The quality control department at Bender Electronics first randomly selects one box from each shipment and then randomly selects 5 keyboards from that box. The shipment is accepted if not more than 1 of the 5 keyboards is defective. The quality control inspector at Bender Electronics selected a box from a recently received shipment of keyboards. Unknown to the inspector, this box contains 6 defective keyboards. a. What is the probability that this shipment will be accepted? b. What is the probability that this shipment will not be accepted?
According to a March 25,2007 Pittsburgh Post-Gazette article, \(30 \%\) to \(40 \%\) of U.S. taxpayers cheat on their returns. Suppose that \(30 \%\) of all current U.S. taxpayers cheat on their returns. Use the binomial probabilities table (Table I of Appendix C) or technology to find the probability that the number of U.S. taxpayers in a random sample of 14 who cheat on their taxes is a. at least 8 \(\mathrm{b}\), at most 3 c. 3 to 7
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