Question

The average time taken for your Internet service provider to remotely resolve a trouble ticket has a Normal distribution, with a mean of 4.3 hours and a standard deviation of 3.1 hours. What percent of the time can you expect to wait longer than a full (8-hour) business day for a resolution?

Answer 1

Answer: 11.63%

Step-by-step explanation:

Given : The average time taken for your Internet service provider to remotely resolve a trouble ticket has a Normal distribution with a mean of 4.3 hours and a standard deviation of 4.3 hours.

i.e. $\mu=4.3$  and $\sigma=3.1$

Let x denotes the time taken for your Internet service provider to remotely resolve a trouble ticket ( in hours).

The probability  time can you expect to wait longer than a full (8-hour) business day for a resolution :

$P(x>8)=1-P(\leq8)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{8-4.3}{3.1})\\\\=1-P(z\leq1.1935)\ \ [\because\ z=\dfrac{x-\mu}{\sigma}]\\\\ =1-0.8837\ \ [\text{By z-table}]\\\\=0.1163=11.63\%$

Therefore , the percent of the time can you expect to wait longer than a full (8-hour) business day for a resolution = 11.63%