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 7 5 0.14 6 0.3 7 0.36 8 0.06 1 2 4

Explanation:

Step1: Recall total probability

The sum of all probabilities in a probability distribution is \( 1 \). Let the probability for \( X = 4 \) be \( p \). So, \( 0.1 + p + 0.14 + 0.3 + 0.36 + 0.06 = 1 \).

Step2: Calculate the probability for \( X = 4 \)

Simplify the left - hand side: \( 0.1+0.14 + 0.3+0.36+0.06=0.96 \). Then \( p=1 - 0.96 = 0.04 \). Wait, there is a typo in the table, it should be \( 0.04 \) instead of \( 7 \) (probably a decimal point error).

Step3: Find the number of employees

The number of employees who work 4 hours is the total number of employees (50) multiplied by the probability of working 4 hours. So \( 50\times0.04 = 2 \).

Answer:

2