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Chapter 4: Q. 44 (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 theU.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 least two of the freshmen reply鈥测别蝉鈥�?

Short Answer

Expert verified

The probability that at least two of the freshmen reply"yes" is0.999.

Step by step solution

01

Given information

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

02

Explanation

The probability of at least two successes out of eight trials is :

PX=x=nxpxqn-x;0鈮�p鈮�1,x=0,1,2,鈥�,n,q=1-pPX鈮�2=1-PX<2=1-P0+P1=1-0.00096=0.999

Thus, the probability that at least two of the freshmen reply"yes" is 0.999, which is approximately 1. So, the event that at least two of the freshmen reply"yes" is almost sure.

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Most popular questions from this chapter

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 values does the random variable 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.

On average (渭), how many freshmen would you expect to have to ask until you found one who replies "yes?"

It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose we are interested in the number of California residents we must survey until we find a resident who does not have adequate earthquake supplies.

a. In words, define the random variable X.

b. List the values that X may take on.

c. Give the distribution of X. X ~ _____(_____,_____)

d. What is the probability that we must survey just one or two residents until we find a California resident who does not have adequate earthquake supplies?

e. What is the probability that we must survey at least three California residents until we find a California resident who does not have adequate earthquake supplies?

f. How many California residents do you expect to need to survey until you find a California resident who does not have adequate earthquake supplies?

g. How many California residents do you expect to need to survey until you find a California resident who does have adequate earthquake supplies?

Suppose that the PDF for the number of years it takes to earn a Bachelor of Science (B.S.) degree is given as in Table 4.34

On average, how many years do you expect it to take for an individual to earn a B.S.?

We know that for a probability distribution function to be discrete, it must have two characteristics. One is that the sum of the probabilities is one. What is the other characteristic?

Use the following information to answer the next five exercises: Javier volunteers in community events each month. He does not do more than five events in a month. He attends exactly five events 35%of the time, four events 25%of the time, three events 20%of the time, two events 10%of the time, one event 5%of the time, and no events 5% of the time.
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