Question

use the probability distribution to complete parts (a) through (e). the probability distribution of the number of overtime hours worked in one week per employee
x 0 1 2 3 4 5 6
p(x) 0.026 0.052 0.151 0.307 0.198 0.161 0.105
(a) find the probability of randomly selecting an employee whose overtime is one or two hours. the probability is 0.203. (type an integer or a decimal. do not round.)
(b) find the probability of randomly selecting an employee whose overtime is two hours or less. the probability is . (type an integer or a decimal. do not round.)

Explanation:

Step1: Identify relevant probabilities

We need $P(0)$, $P(1)$ and $P(2)$. Given $P(0)=0.026$, $P(1) = 0.052$, $P(2)=0.151$.

Step2: Use addition - rule for mutually - exclusive events

For mutually - exclusive events, $P(X\leq2)=P(0)+P(1)+P(2)$.
$P(0)+P(1)+P(2)=0.026 + 0.052+0.151$
$=0.229$

Answer:

$0.229$