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Chapter 4: Q. 48 (page 286)

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 “yes.” 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(1−p)x−1;0≤p≤1,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

A hospital researcher is interested in the number of times the average post-op patient will ring the nurse during a 12-hour shift. For a random sample of 50 patients, the following information was obtained. What is the expected value?

Complete Table 4.28 using the data provided.

An emergency room at a particular hospital gets an average of five patients per hour. A doctor wants to know the probability that the ER gets more than five patients per hour. Give the reason why this would be a Poisson distribution.

According to a Gallup poll, 60% of American adults prefer saving over spending. Let X = the number of American adults out of a random sample of 50 who prefer saving to spending.

a. What is the probability distribution for X?

b. Use your calculator to find the following probabilities:

i. the probability that 25 adults in the sample prefer saving over spending

ii. the probability that at most 20 adults prefer saving

iii. the probability that more than 30 adults prefer saving

c. Using the formulas, calculate the

(i) mean and

(ii) standard deviation of X.

A fair, six-sided die is rolled ten times. Each roll is independent. You want to find the probability of rolling a one more than three times. State the probability question mathematically.
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