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# Probability in Situations Given

A company that has 327 employees chooses a committee of 17 to represent employee retirement issues. When the committee was formed, none of the 83 minority employees were selected.
1. Find the number of ways 17 employees can be chosen from 327.
2. Find the number of ways 17 employees can be chosen from 244 non-minorities.
3. If the committee was chosen randomly (without bias), what is the probability that it contained no minorities?
4. Does your answer to question 3 indicate that the committee selection process is biased?

Use the following information to answer problems 5-8.
A warehouse employs 47 workers on the first shift and 22 workers on the second shift.
Eleven workers are chosen at random to be interviewed about the work environment. Find the following probabilities.
5. The probability that all are first-shift workers.
6. The probability that all are second-shift workers.
7. The probability that there are five first-shift workers.
8. The probability that there are four second-shift workers.

Use the following information to answer problem 9.
The number of computers per household in a small town:
# of Computers 0 1 2 3
# of Households 453 272 109 40
9. Unusual values: A person lives in the small town described above and in a household with two computers. He claims that having two computers is unusual. Is this person correct? Why?

Use the following information to answer problems 10-15.
One in eight adults says he or she has no trouble sleeping at night. You randomly select six adults and ask if he or she has no trouble sleeping at night.
10. Construct a binomial distribution.
11. Graph the binomial distribution using a histogram.
12. Describe the shape of the histogram.
13. Find the mean of the binomial distribution.
14. Find the variance of the binomial distribution.
15. Find the standard deviation of the binomial distribution.

#### Solution Preview

Included is the explanation in the Word document.

A company that has 327 employees chooses a committee of 17 to represent employee retirement issues. When the committee was formed, none of the 83 minority employees were selected.
1. Find the number of ways 17 employees can be chosen from 327.
The total number of employees is 327 and 17 employees are selected. In this case, the order is not important.
Therefore, the total ways are 327C17=1.02921*10^28

2. Find the number of ways 17 employees can be chosen from 244 non-minorities.
The total ways are 244C17=6.12131*10^25

3. If the committee was chosen randomly (without bias), what is the probability that it contained no minorities?
1-6.12131*10^25/(1.02921*10^28)=0.99405

4. Does your answer to question 3 indicate that the committee selection process is biased?
Since the probability that it contained no minorities is 0.99405, close to 1, it definitely ...

#### Solution Summary

The solution discusses probability in situations given.

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