Respuesta :
Answer:
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 [tex]P(X = 3) = 0.16[/tex]
60% chance of hiring at least two candidates.
This means that:
[tex]P(X = 2) + P(X = 3) = 0.6[/tex]
[tex]P(X = 2) + 0.16 = 0.6[/tex]
[tex]P(X = 2) = 0.44[/tex]
Probability of one hire:
The sum of all probabilities, from no hires to three hires, is 1. So
[tex]P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) = 1[/tex]
[tex]0.06 + P(X = 1) + 0.16 + 0.44 = 1[/tex]
[tex]P(X = 1) = 0.66 = 1[/tex]
[tex]P(X = 1) = 0.34[/tex]
a. What is the probability that the firm will make at least one hire?
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.06 = 0.94[/tex]
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:
[tex]E(X) = 0.06*0 + 0.34*1 + 0.44*2 + 0.16*3 = 1.7[/tex]
Standard deviation:
[tex]S(X) = \sqrt{0.06*(0-1.7)^2 + 0.34*(1-1.7)^2 + 0.44*(2-1.7)^2 + 0.16*(3-1.7)^2} = 0.8062[/tex]
The expected value of the number of hires is 1.7, and the standard deviation is 0.8062.
