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Use the following information to answer the next six exercises: The Higher Education Research Institute at UCLA collected data from203,967 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.

Construct the probability distribution function (PDF). Stop at x = 6.

Short Answer

Expert verified

The probability distribution function (PDF)

Step by step solution

01

Introduction

a probability distribution is a numerical capacity that gives the probabilities of events of various potential results for an experiment. It is a numerical portrayal of an arbitrary peculiarity as far as its example space and the probabilities of occasions

02

explanation 

UsingP(X=x)=p(1p)x1;0p1,x=1,2,3,4,5,6

we calculate the probability of x trials,

Substituting the values of x in the formula, we get the probability distribution function (PDF)

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Most popular questions from this chapter

Suppose that a technology task force is being formed to study technology awareness among instructors. Assume that ten people will be randomly chosen to be on the committee from a group of 28 volunteers, 20 who are technically proficient and eight who are not. We are interested in the number on the committee who are not technically proficient.

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. How many instructors do you expect on the committee who are not technically proficient?

e. Find the probability that at least five on the committee are not technically proficient.

f. Find the probability that at most three on the committee are not technically proficient.

Approximately 8%of students at a local high school participate in after-school sports all four years of high school. A group of 60seniors is randomly chosen. Of interest is the number that participated in after-school sports all four years of

high school.

a. In words, define the random variable X.

b. List the values that Xmay take on.

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

d. How many seniors are expected to have participated in after-school sports all four years of high school?

e. Based on numerical values, would you be surprised if none of the seniors participated in after-school sports all

four years of high school.

f. Based on numerical values, is it more likely that four or that five of the seniors participated in after-school sports

all four years of high school? Justify your answer numerically.

A trainer is teaching a dolphin to do tricks. The probability that the dolphin successfully performs the trick is 35%, and the probability that the dolphin does not successfully perform the trick is 65%. Out of 20 attempts, you want to find the probability that the dolphin succeeds 12 times. State the probability question mathematically.

Construct a PDF table.

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.?

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