A public interest group hires students to solicit donations by telephone. After a brief training period students make calls to potential donors and are paid on a commission basis. Experience indicates that early on, these students tend to have only modest success and that 75% of them give up their jobs in their first two weeks of employment. The group hires 7 students, which can be viewed as a random sample. Answer parts a. and b. below.

Question

A public interest group hires students to solicit donations by telephone. After a brief training period students make calls to potential donors and are paid on a commission basis. Experience indicates that early on, these students tend to have only modest success and that 75% of them give up their jobs in their first two weeks of employment. The group hires 7 students, which can be viewed as a random sample. Answer parts a. and b. below.

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Part 1
a. What is the probability that at least 2 of the 7 will give up in the first two weeks?

Answer 1

To calculate the probability that at least 2 out of the 7 students will give up in the first two weeks, we can use the complement rule and find the probability that fewer than 2 students give up.

First, calculate the probability that exactly 0 or 1 student gives up:
Probability(0 students give up) = (0.75)^7
Probability(1 student gives up) = 7C1 * (0.75)^6 * (0.25)^1

Then, sum these probabilities:
Probability(0 or 1 student gives up) = Probability(0 students give up) + Probability(1 student gives up)

Finally, to find the probability that at least 2 students give up, subtract the probability of 0 or 1 student giving up from 1:
Probability(at least 2 students give up) = 1 - Probability(0 or 1 student gives up)

You can calculate and get the final result.