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Chapter 4: Q. 53 (page 287)

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.

What values does Xtake on?

Short Answer

Expert verified

The continuous random variable can have any number of values.x=2,3,4,5,6,7,8,9

Step by step solution

01

Given

From a total of 16business majors and 7non-business majors, a sample of 9students was chosen. The random variable's representation of the data:

X: The sample's number of business majors.

02

Explanation of Solution

A discrete random variable is X. Because there are only 7non-business students in the group, the sample of size 9will have at least 2business majors. As a result, the lowest number that Xcan take is 2. It's also possible that all of the students chosen are business majors, in which case the maximum value for x is 9. As a result, any integral value between 2and 9can be assigned to the random variableX. (both inclusive).

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Most popular questions from this chapter

Suppose that the probability that an adult in America will watch the Super Bowl is 40%. Each person is considered independent. We are interested in the number of adults in America we must survey until we find one who will watch the Super Bowl.

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 adults in America do you expect to survey until you find one who will watch the Super Bowl?

e. Find the probability that you must ask seven people.

f. Find the probability that you must ask three or four people

What does the column “P(x)” sum to?

Use the following information to answer the next six exercises: A baker is deciding how many batches of muffins to make to

sell in his bakery. He wants to make enough to sell every one and no fewer. Through observation, the baker has established

a probability distribution.

P(x≥5)

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

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 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? Justify your answer numerically.

f. Based upon 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 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?
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