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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.

Find the standard deviation.

Short Answer

Expert verified

The standard deviation of the gaussian random Xdistributions is 1.1012.

Step by step solution

01

Formula used

The standard deviation of a hypergeometric distribution with parameters r,b&nis given by:

σ=rbn(r+b-n)(r+b)2(r+b-1)

02

Given

The values we are having:

r=16,b=7andn=9

03

Calculation

The standard deviation is calculated by multiplying r=16,b=7andn=9in the given formula:

localid="1649709225134" σ=16×7×9(16+7-9)(16+7)2(16+7-1)=1.1012

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Most popular questions from this chapter

For the given values of the random variable X, fill in the corresponding probabilities

More than 96 percent of the very largest colleges and universities (more than 15,000 total enrollments) have some online offerings. Suppose you randomly pick 13 such institutions. We are interested in the number that offer distance learning courses.

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. On average, how many schools would you expect to offer such courses?

e. Find the probability that at most ten offer such courses.

f. Is it more likely that 12 or that 13 will offer such courses? Use numbers to justify your answer numerically and answer in a complete sentence.

A palette has 200 milk cartons. Of the 200 cartons, it is known that ten of them have leaked and cannot be sold. A stock clerk randomly chooses 18 for inspection. He wants to know the probability that among the 18, no more than two are leaking. Give five reasons why this is a hypergeometric problem.

Find the standard deviation.

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.

On average (μ), how many would you expect to be business majors?

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