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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

Use the following information to answer the next six exercises: The Higher Education Research Institute at UCLA collected data from 203,967 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.

What values does the random variable X take on?

It has been estimated that only about 30% of California residents have adequate earthquake supplies. Suppose you randomly survey 11 California residents. We are interested in the number who have adequate earthquake supplies.

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. What is the probability that at least eight have adequate earthquake supplies?

e. Is it more likely that none or that all of the residents surveyed will have adequate earthquake supplies? Why?

f. How many residents do you expect will have adequate earthquake supplies?

A lacrosse team is selecting a captain. The names of all the seniors are put into a hat, and the first three that are drawn will be the captains. The names are not replaced once they are drawn (one person cannot be two captains). You want to see if the captains all play the same position. State whether this is binomial or not and state why.

Suppose that about 85% of graduating students attend their graduation. A group of 22 graduating students is randomly chosen.

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 are expected to attend their graduation?

e. Find the probability that 17 or 18 attend.

f. Based on numerical values, would you be surprised if all 22 attended graduation? Justify your answer numerically

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’s say that you buy one of Pierre’s 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?

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