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Chapter 4: Q. 43 (page 286)

Use the following information to answer the next eight exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly pick eight first-time, full-time freshmen from the survey. You are interested in the number that believes that same sex-couples should have the right to legal marital status.

What is the probability that at most five of the freshmen reply鈥测别蝉鈥�?

Short Answer

Expert verified

The probability that at most five of the freshmen reply"yes" is0.4151.

Step by step solution

01

Given information

n=8,p=0.713,q=1-0.713=0.287

02

Explanation

The probability of at most five successes out of eight trials is:

PX=x=xnpxqn-x;0鈮�p鈮�1,x=0,1,2,鈥�,n,q=1-pPX鈮�5=P0+P2+P3+P4+P5PX鈮�5=0.4151

Thus, the probability that at most five of the freshen reply "yes" is 0.4151.

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Most popular questions from this chapter

You are playing a game of chance in which four cards are drawn from a standard deck of 52 cards. You guess the suit of each card before it is drawn. The cards are replaced in the deck on each draw. You pay \(1 to play. If you guess the right suit every time, you get your money back and \)256. What is your expected profit of playing the game over the long term?

You throw darts at a board until you hit the center area. Your probability of hitting the center area is p = 0.17. You want to find the probability that it takes eight throws until you hit the center. What values does X take on?

Use the following information to answer the next six exercises: The Higher Education Research Institute at UCLA collected data from 203,967 incoming first-time, full-time freshmen from 270 four-year colleges and universities in the U.S. 71.3% of those students replied that, yes, they believe that same-sex couples should have the right to legal marital status. Suppose that you randomly select freshman from the study until you find one who replies 鈥測es.鈥� You are interested in the number of freshmen you must ask.

What is the probability that you will need to ask fewer than three freshmen?

Define the random variableX .

Identify the mistake in the probability distribution table.

Use the following information to answer the next five exercises: A physics professor wants to know what percent of physics

majors will spend the next several years doing post-graduate research. He has the following probability distribution.
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