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. [tex]\mu=4.3[/tex] and [tex]\sigma=3.1[/tex]
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 :
[tex]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\%[/tex]
Therefore , the percent of the time can you expect to wait longer than a full (8-hour) business day for a resolution = 11.63%
