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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“yes”?

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;0p1,x=0,1,2,,n,q=1-pPX5=P0+P2+P3+P4+P5PX5=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

For the given values of the random variable X, fill in the corresponding probabilities

A customer service center receives about ten emails every half-hour. What is the probability that the customer service center receives more than four emails in the next six minutes? Use the TI-83+ or TI-84 calculator to find the answer.

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 “yes.” You are interested in the number of freshmen you must ask.

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