a manager records the number of hours, x, each employee works on his or her shift and develops the…
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?\nprobability distribution\nhours worked: x\tprobability: p(x)\n3\t0.1\n4\t?\n5\t0.14\n6\t0.3\n7\t0.36\n8\t0.06\n0\n1\n2\n4
Answer
Explanation:
Step1: Find probability of working 4 hours
Since sum of all probabilities in a probability - distribution is 1. Let $P(4)$ be the probability of working 4 hours. Then $P(4)=1-(0.1 + 0.14+0.3 + 0.36+0.06)=1 - 0.96 = 0.04$.
Step2: Calculate number of people working 4 hours
We know there are 50 people in total. The number of people working 4 hours is $n = 50\times P(4)$. Substitute $P(4)=0.04$ into the formula, we get $n = 50\times0.04=2$.
Answer:
2