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Complete Table 4.28 using the data provided.

Short Answer

Expert verified

The probability distribution table:

Step by step solution

01

Given Information

A ballet trainer wants to know how many students from each year's class will return the following year so she can prepare what lessons to provide. She's developed a working probability throughout the seasons, where X signifies the number of years a person will learn ballet with the teacher and P(X) denotes the probability of learning for such years.

02

Concept Used

The combination of a Random Variable's chances of values taken adds up to 1.

03

Calculation

Because the total of probability equals 1

0.10+0.05+0.10+P(4)+0.30+0.20+0.10=1

that is, role="math" localid="1648458749075" P(4)+0.85=1

role="math" localid="1648458925787" P(4)=1-0.85=0.15x multiplied with p(x) yields the third column.

that is, (1)(0.10)=0.10,(2)(0.05)=0.10

04

Explanation

The table below is the result of putting in the values of P(4).

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Most popular questions from this chapter

Ellen has music practice three days a week. She practices for all of the three days 85% of the time, two days 8% of the time, one day 4% of the time, and no days 3% of the time. One week is selected at random. What values does X take on?

On May 11, 2013 at 9:30 PM, the probability that moderate seismic activity (one moderate earthquake) would occur in the next 48hours in Japan was about 1.08%. As in Example 4.8, you bet that a moderate earthquake will occur in Japan during this period. If you win the bet, you win \(100. If you lose the bet, you pay\)10. Let X = the amount of profit from a bet. Find the mean and standard deviation of X.

An electronics store expects to have ten returns per day on average. The manager wants to know the probability of the store getting fewer than eight returns on any given day. State the probability question mathematically.

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.

Identify the mistake in the probability distribution table.

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