Red Widget Strategies wants to improve its customer service by being more efficient in how...

Solution:
Given that,
$$\begin{gathered} \mu = 240 \\ \sigma = 40 \\ N = 1000 \end{gathered}$$
$$\begin{gathered} p ( x < 180 ) \\ = p ( x - \frac{\mu }{\sigma }) < ( 180 - \frac{240}{40}) \\ = p ( z < - \frac{60}{40}) \\ = p ( z < - 1. 5 ) \end{gathered}$$
Using z table
$$\begin{gathered} = 0.0668 \cdot N \\ = 0.0668 \cdot 1000 \end{gathered}$$
Probability = 66.8
b) $$\begin{gathered} p ( 180 < x < 300 ) \\ = p ( 180 - \frac{240}{40}) < ( x - \frac{\mu }{\sigma }) < ( 300 - \frac{240}{40}) \\ = p ( - \frac{60}{40}< z < \frac{60}{40}) \\ = p ( - 1.5 < z < 1.5 ) \\ = p ( z < 1.5 ) - p ( z < 1.5 ) \end{gathered}$$
Using z table
$$\begin{gathered} = 0.9332 - 0.0668 \\ = 0.8664 \cdot N \\ = 0.8664 \cdot 1000 \end{gathered}$$
Probability = 866.4
c) $$\begin{gathered} p ( 110 < x < 180 ) \\ = p ( ( 110 - \frac{240}{40}) < ( x - \frac{\mu }{\sigma }) < ( 180 - \frac{240}{40}) \\ = p ( - \frac{130}{40}< z < - \frac{60}{40}) \\ = p ( - 3.25 < z < - 1.5 ) \\ = p ( z < - 1.5 ) - p ( z < - 3.25 ) \end{gathered}$$
Using z table
$$\begin{gathered} = 0.0668 - 0.0006 \\ = 0.0662 \cdot N \\ = 0.0662 \cdot 1000 \end{gathered}$$
Probability = 66.2
d) $$\begin{gathered} p ( x > 300 ) \\ = 1 - p ( x < 300 ) \\ = 1 - p ( x - \frac{\mu }{\sigma }) < ( 300 - \frac{240}{40}) \\ = 1 - p ( z < \frac{60}{40}) \\ = 1 - p ( z < 1. 5 ) \end{gathered}$$
Using z table
$$\begin{gathered} = 1 - 0.9332 \\ = 0.0668 \ast N \\ = 0.0668 \ast 1000 \end{gathered}$$
Probability = 66.8