A company that has 200 employees chooses a committee of 15 to represent employee retirement issues. When the committee is formed, none of the 56 minority employees are selected. (a) Use technology to find the number of ways 15 employees can be chosen from 200. (b) Use technology to find the number of ways 15 employees can be chosen from 144 nonminorities. (c) What is the probability that the committee contains no minorities when the committee is chosen randomly (without bias)? (d) Does your answer to (c) indicate that the committee selection is biased? Explain your reasoning.

MATLAB: An Introduction with Applications
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### Probability and Statistics Problem

A company that has 200 employees chooses a committee of 15 to represent employee retirement issues. When the committee is formed, none of the 56 minority employees are selected.

#### Tasks:
(a) **Use technology to find the number of ways 15 employees can be chosen from 200.**  
- Answer: There are \(\_\_\_\_\) ways to choose 15 employees from 200 employees.  
  *(Use scientific notation. Round to two decimal places as needed. Use the multiplication symbol in the math palette as needed.)*

(b) **Use technology to find the number of ways 15 employees can be chosen from 144 nonminorities.**
- Answer: There are \(\_\_\_\_\) ways to choose 15 employees from 144 nonminorities.  
  *(Use scientific notation. Round to two decimal places as needed. Use the multiplication symbol in the math palette as needed.)*

(c) **What is the probability that the committee contains no minorities when the committee is chosen randomly (without bias)?**
- Answer: The probability is \(\_\_\_\_\)  
  *(Do not round until the final answer. Then round to three decimal places as needed.)*

(d) **Does your answer to (c) indicate that the committee selection is biased? Explain your reasoning.**
- Answer: \(\_\_\_\_\) the committee selection is most likely \(\_\_\_\_\) because the probability that was found in part (c) is \(\_\_\_\_\).

**Note:** Enter your answer in each of the answer boxes.

This problem allows students to explore combinations and probabilities using real-world scenarios. Understanding these concepts helps in analyzing and assessing fairness in selection processes.
Transcribed Image Text:### Probability and Statistics Problem A company that has 200 employees chooses a committee of 15 to represent employee retirement issues. When the committee is formed, none of the 56 minority employees are selected. #### Tasks: (a) **Use technology to find the number of ways 15 employees can be chosen from 200.** - Answer: There are \(\_\_\_\_\) ways to choose 15 employees from 200 employees. *(Use scientific notation. Round to two decimal places as needed. Use the multiplication symbol in the math palette as needed.)* (b) **Use technology to find the number of ways 15 employees can be chosen from 144 nonminorities.** - Answer: There are \(\_\_\_\_\) ways to choose 15 employees from 144 nonminorities. *(Use scientific notation. Round to two decimal places as needed. Use the multiplication symbol in the math palette as needed.)* (c) **What is the probability that the committee contains no minorities when the committee is chosen randomly (without bias)?** - Answer: The probability is \(\_\_\_\_\) *(Do not round until the final answer. Then round to three decimal places as needed.)* (d) **Does your answer to (c) indicate that the committee selection is biased? Explain your reasoning.** - Answer: \(\_\_\_\_\) the committee selection is most likely \(\_\_\_\_\) because the probability that was found in part (c) is \(\_\_\_\_\). **Note:** Enter your answer in each of the answer boxes. This problem allows students to explore combinations and probabilities using real-world scenarios. Understanding these concepts helps in analyzing and assessing fairness in selection processes.
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