Mathematical Statistics with Applications
Mathematical Statistics with Applications
7th Edition
ISBN: 9781111798789
Author: Dennis O. Wackerly
Publisher: Cengage Learning
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Chapter 1, Problem 32SE
To determine

Prove that the fraction of observations within the interval y¯ks and y¯+ks is at least 11k2.

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59. At a certain gas station, 40% of the customers use regular gas (A1), 35% use plus gas (A2), and 25% use premium (A3). Of those customers using regular gas, only 30% fill their tanks (event B). Of those customers using plus, 60% fill their tanks, whereas of those using premium, 50% fill their tanks.a. What is the probability that the next customer will request plus gas and fill the tank (A2 B)?b. What is the probability that the next customer fills the tank?c. If the next customer fills the tank, what is the probability that regular gas is requested? Plus? Premium?
38. Possible values of X, the number of components in a system submitted for repair that must be replaced, are 1, 2, 3, and 4 with corresponding probabilities .15, .35, .35, and .15, respectively. a. Calculate E(X) and then E(5 - X).b. Would the repair facility be better off charging a flat fee of $75 or else the amount $[150/(5 - X)]?  [Note: It is not generally true that E(c/Y) = c/E(Y).]
74. The proportions of blood phenotypes in the U.S. popula- tion are as follows:A     B    AB   O .40 .11  .04  .45 Assuming that the phenotypes of two randomly selected individuals are independent of one another, what is the probability that both phenotypes are O? What is the probability that the phenotypes of two randomly selected individuals match?

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