Question

a manager records the number of hours, x, each employee works on his or her shift and develops the probability distribution below. fifty people work for the manager. how many people work 4 hours per shift? probability distribution hours worked: x probability: p(x) 3 0.1 4 ? 5 0.14 6 0.3 7 0.36 8 0.06 0 1 2 4

Explanation:

Step1: Find the probability of working 4 hours

The sum of all probabilities in a probability distribution is \(1\). Let \(P(4)\) be the probability of working 4 hours.

$$P(3)+P(4)+P(5)+P(6)+P(7)+P(8) = 1$$

$$0.1+P(4)+0.14 + 0.3+0.36+0.06=1$$

$$P(4)=1-(0.1 + 0.14+0.3+0.36+0.06)$$

$$P(4)=1 - 0.96$$

$$P(4)=0.04$$

Step2: Calculate the number of people working 4 hours

If there are \(n = 50\) people in total, and the probability of working 4 hours is \(P(4)=0.04\), then the number of people \(N\) working 4 hours is given by \(N=n\times P(4)\)

$$N = 50\times0.04$$

$$N=2$$

Answer:

\(2\)