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Chapter 6: Q. 2.1 (page 390)

To introduce her class to binomial distributions, Mrs. Desai gives a 10 -item, multiple-choice quiz. The catch is, that students must simply guess an answer (A through E) for each question. Mrs. Desai uses her computer's random number generator to produce the answer key so that each possible answer has an equal chance to be chosen. Patti is one of the students in this class. Let X=the number of Patti's correct guesses.

1. Show that Xis a binomial random variable.

Short Answer

Expert verified

It has been shown thatXis a binomial random variable.

Step by step solution

01

Given Information 

Mr. Desai gives =10times

X=The number of Patti's correct guesses.

02

Explanation

The algorithm chose correct responses at random, thus one trial should not alter the outcome of the others.

There were ten questions in total.

Each trial has a0.20 chance of succeeding.

As a result, this is a binomial situation.

Because it counts the number of successes, Xis a binomial random variable withn=10and p=0.20.

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Most popular questions from this chapter

52. Study habits The academic motivation and study habits of female students as a group are better than those of males. The Survey of Study Habits and Attitudes (SSHA)is a psychological test that measures these factors. The distribution of SSHAscores among the women at a college has mean120and standard deviation 28, and the distribution of scores among male students has mean 105and standard deviation 35.You select a single male student and a single female student at random and give them theSSHA test.
(a) Explain why it is reasonable to assume that the scores of the two students are independent.
(b) What are the expected value and standard deviation of the difference (female minus male) between their scores?
(c) From the information given, can you find the probability that the woman chosen scores higher than the man? If so, find this probability. If not,
explain why you cannot.

Binomial setting? A binomial distribution will be approximately correct as a model for one of these two sports settings and not for the other. Explain why by briefly discussing both settings. (a) A National Football League kicker has made 80%of his field-goal attempts in the past. This season he attempts 20field goals. The attempts differ widely in the distance, angle, wind, and so on. (b) A National Basketball Association player has made 80%of his free-throw attempts in the past. This season he takes 150free throws. Basketball free throws are always attempted from 15feet away with no interference from other players

Ana is a dedicated Skee Ballplayer (see photo) who always rolls for the 50-point slot. The probability distribution of Ana's score Xon a single roll of the ball is shown below. You can check that μX=23.8and σX=12.63.

(a) A player receives one ticket from the game for every 10points scored. Make a graph of the probability distribution for the random variable T=number of tickets Ana gets on a randomly selected throw. Describe its shape.

(b) Find and interpret μT.

(c) Compute and interpret σT.

In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p?

(a)n=10,p=0.5

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76. Rhubarb Suppose you purchase a bundle of 10bare-root rhubarb plants. The sales clerk tells you that on average you can expect 5%of the plants to die before producing any rhubarb. Assume that the bundle is a random sample of plants. Let Y= the number of plants that die before producing any rhubarb. Use the binomial probability formula to find
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