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Chapter 5: Q 5.152. (page 242)
Discuss the pros and cons of binomial probability tables.
It avoids the calculations and it contains only a small number of combinations of n and p.
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Persons per Housing Unit. From the document American Housing Survey for the United States, published by the U.S. Census Bureau, we obtained the following frequency distribution for the number of persons per occupied housing unit, where we have used "7" in place of 鈥�7 or more.鈥� Frequencies are in millions of housing units.
| Person | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Frequencies | 27.9 | 34.4 | 17.0 | 15.5 | 6.8 | 2.3 | 1.4 |
For a randomly selected housing unit, let Y denote the number of persons living in that unit.
a. Identify the possible values of the random variable Y.
b. Use random-variable notation to represent the event that a housing unit has exactly three persons living in it.
c. Determine P(Y = 3); interpret in terms of percentages.
d. Determine the probability distribution of Y.
e. Construct a probability histogram for Y.
Sample Size for Proportion Find the sample size required to estimate the percentage of college students who take a statistics course. Assume that we want 95% confidence that the proportion from the sample is within four percentage points of the true population percentage.
Pets. According to JAVMA News, a publication of the American Veterinary Medical Association, roughly 60% of U.S. households own one or more pets. Four U.S. households are selected at random. Use Table VII in Appendix A to solve the following problems.
(a) Find the probability that, of the four households sampled, the number that own one or more pets is exactly three; at least three; at most three.
(b) Find the probability distribution of the random variable X. the number of U.S. households in a random sample of four that own one or more pets.
(c) Without referring to the probability distribution obtained in part (b) or constructing a probability histogram, decide whether the probability distribution is right-skewed, symmetric, or left-skewed. Explain your answer. *
Committee Selection. Refer to the image below for each of the following events, list the outcomes that constitute the event, and describe the event in words.
a. (not A)
b. (B&D)
c. (B or C)
A committee consists of five executives, three women and two men. Their names are Maria (M), John (J), Susan (S), Will (W), and Holly (H). The committee needs to select a chairperson and a secretary. It decides to make the selection randomly by drawing straws. The person getting the longest straw will be appointed chairperson, and the one getting the shortest straw will be appointed secretary. The possible outcomes can be represented in the following manner.
In Exercise 5.129 - 5.132, We have provided the probability distributions of the random variables considered in Exercise 5.109 - 5.112 of section 5.4 For each exercise, do the following tasks.
Part (a) Find the mean of the random variable.
Part (b) Obtain the standard deviation of the random variable by using one of the formulas given in definition 5.10.
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