A marketing firm is considering making up to three new hires. Given its specific needs, the management feels that there is a 60% chance of hiring at least two candidates. There is only a 6% chance that it will not make any hires and a 16% chance that it will make all three hires. Required:
a. What is the probability that the firm will make at least one hire?
b. Find the expected value and the standard deviation of the number of hires.

a. 0.94 = 94% probability that the firm will make at least one hire.

b. The expected value of the number of hires is 1.7, and the standard deviation is 0.8062.

Step-by-step explanation:

There is only a 6% chance that it will not make any hires

This means that P(X = 0) = 0.06.

16% chance that it will make all three hires.

This means that

60% chance of hiring at least two candidates.

This means that:

Probability of one hire:

The sum of all probabilities, from no hires to three hires, is 1. So

a. What is the probability that the firm will make at least one hire?

0.94 = 94% probability that the firm will make at least one hire.

b. Find the expected value and the standard deviation of the number of hires.

Expected value:

Standard deviation:

The expected value of the number of hires is 1.7, and the standard deviation is 0.8062.