Solution Found!
Constructing and Graphing Discrete Probability
Chapter 4, Problem 20E(choose chapter or problem)
(a) construct a probability distribution, and (b) graph the probability distribution using a histogram and describe its shape.
Overtime Hours
The number of overtime hours worked in one week per employee
\(\begin{array}{|l|c|c|c|c|c|c|c|} \hline \text { Overtime hours } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Employees } & 6 & 12 & 29 & 57 & 42 & 30 & 16 \\ \hline \end{array}\)
Questions & Answers
QUESTION:
(a) construct a probability distribution, and (b) graph the probability distribution using a histogram and describe its shape.
Overtime Hours
The number of overtime hours worked in one week per employee
\(\begin{array}{|l|c|c|c|c|c|c|c|} \hline \text { Overtime hours } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Employees } & 6 & 12 & 29 & 57 & 42 & 30 & 16 \\ \hline \end{array}\)
ANSWER:Step1 of 3:
From the given problem we have a data set and iit is given below:
\(\begin{array}{|l|c|c|c|c|c|c|c|} \hline \text { Overtime hours } & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline \text { Employees } & 6 & 12 & 29 & 57 & 42 & 30 & 16 \\ \hline \end{array}\)
Here our goal is:
a). We need to construct a probability distribution.
b). We need to graph the probability distribution using a histogram and describe its shape.
Step2 of 3:
a). Consider,
\(\begin{array}{|c|c|c|} \hline \text { Overtime hours } & \text { Employees } & \text { Probability distribution } \mathrm{P}(\mathrm{X}) \\ \hline 0 & 6 & \frac{6}{192}=0.03125 \\ \hline 1 & 12 & \frac{12}{192}=0.0625 \\ \hline 2 & 29 & \frac{29}{192}=0.151041667 \\ \hline 3 & 57 & \frac{5