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Chapter 4: Q.21 (page 284)

Identify the mistake in the probability distribution table.

Short Answer

Expert verified

Sum of columnP(X)isnot1.

Step by step solution

01

Given Information

Sam volunteers in community events on each month. He only participates in five events at a time. in a month. He joins exactly five events 35%of time, four events 25%of time, three events 20%of time, two events 10%of time, one event 5%of time and no events 5%of time.

02

Explanation

The preceding probability distribution table contains an error in that the total of the P(X)column will not add up to1.

This is because

0.15+0.25+0.30+0.20+0.15=1.05

which is not possible. so,

The sum of probability of all values chosen by a random variable is always1.

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Most popular questions from this chapter

Use the following information to answer the next eight 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 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.

On average(渭), how many would you expect to answer yes?

On average, Pierre, an amateur chef, drops three pieces of egg shell into every two cake batters he makes. Suppose

that you buy one of his cakes.

a. In words, define the random variable X.

b. List the values that Xmay take on.

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

d. On average, how many pieces of egg shell do you expect to be in the cake?

e. What is the probability that there will not be any pieces of egg shell in the cake?

f. Let鈥檚 say that you buy one of Pierre鈥檚 cakes each week for six weeks. What is the probability that there will not

be any egg shell in any of the cakes?

g. Based upon the average given for Pierre, is it possible for there to be seven pieces of shell in the cake? Why?

A theater group holds a fund-raiser. It sells 100 raffle tickets for \(5 apiece. Suppose you purchase four tickets. The prize is two passes to a Broadway show, worth a total of \)150.

a. What are you interested in here?

b. In words, define the random variable X.

c. List the values that X may take on.

d. Construct a PDF.

e. If this fund-raiser is repeated often and you always purchase four tickets, what would be your expected average winnings per raffle?

Use the following information to answer the next five exercises: Suppose that a group of statistics students is divided into two groups: business majors and non-business majors. There are 16business majors in the group and seven non-business majors in the group. A random sample of nine students is taken. We are interested in the number of business majors in the sample.

X~_____(_____,_____)

Find the probability that Javier volunteers for at least one event each month.

P(x>0)=_______
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