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Chapter 6: Q. 87 (page 405)

87. Airport security The Transportation Security Administration (TSA) is responsible for airport safety. On some flights, TSA officers randomly select
passengers for an extra security check before boarding. One such flight had 76辫补蝉蝉别苍驳别谤蝉鈥�12in first class and 64in coach class. Some passengers were surprised when none of the 10 passengers chosen for
screening were seated in first class. Can we use a binomial distribution to approximate this probability? Justify your answer.

Short Answer

Expert verified

No binomial distribution to approximate this probability.

Step by step solution

01

Given information

One flight had 76passengers.12in first class and 64in coach class. Some passengers were surprised when none of the 10 passengers chosen for screening were seated in first class.

02

Explanation

A random variable has a binomial distribution if:

  • In terms of variables, there are two possible outcomes.
  • Each draw must be self-contained.
  • There are a set number of elements.

In probability, there is always a chance of success. Because each draw is not independent, persons are chosen without replacement, and the sample size is greater than 10%of the population, Xhas no binomial distribution.

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Most popular questions from this chapter

Suppose you roll a pair of fair, six-sided dice. Let T= the sum of the spots showing on the up-faces.

(a) Find the probability distribution of T.

(b) Make a histogram of the probability distribution. Describe what you see.

(c) Find P(T鈮�5)and interpret the result.

Based on the analysis in Exercise 41, the ferry company decides to increase the cost of a trip to $6. We can calculate the company鈥檚 profit Yon a randomly selected trip from the number of cars X. Find the mean and standard deviation ofY. Show your work.

A test for extrasensory perception (ESP) involves asking a person to tell which of 5shapes鈥攁 circle, star, triangle, diamond, or heart鈥攁ppears on a hidden computer screen. On each trial, the computer is equally likely to select any of the 5shapes. Suppose researchers are testing a person who does not have ESP and so is just guessing on each trial. What is the probability that the person guesses the first 4shapes incorrectly but gets the fifth correct?

a). 1/5

b). 454

c). 45415

d). 5145415

e).4/5

51. His and her earnings A study of working couples measures the income Xof the husband and the income Yof the wife in a large number of couples in which both partners are employed. Suppose that you knew the means 渭Xand 渭Yand the variances 蟽X2and 蟽纬2 of both variables in the population.
(a) Is it reasonable to take the mean of the total income X+Yto be 渭X+渭Y ? Explain your answer.
(b) Is it reasonable to take the variance of the total income to be 蟽X2+蟽y2 ? Explain your answer.

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

(b)n=40,p=0.88

(c)n=100,p=0.2

(d)n=100,p=0.99

(e)n=1000,p=0.003
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