Question

customers experiencing technical difficulties with their wyoming internet cable hookup may call an 1-800 number for technical support. it takes a technician between 30 and 600 seconds to resolve the problem. the distribution of support times follows the uniform probability distribution. (a) what is the expected value time to resolve the problem? (b) what percent of the problems take more than 300 seconds to resolve? (c) what is the standard deviation of the random variable? g

Answer 1

(a) Percentage of problems take less than 300 seconds or 5 minutes =41.77%

(b) 58.23% percent of the problems take more than 300 seconds or 5 minutes to resolve.

(b) Takes the technician between 30 seconds to 600 seconds to resolve the problem.

90 seconds = 90/60 = 1.5 minutes

600 seconds =600/60 =  10 minutes

So,

$\mathrm{x} \sim \mathrm{U}(1.5,10)\\P(x > 5 \min )=?$

$\begin{aligned}& \mathrm{f}(\mathrm{x})=\frac{1}{\mathrm{~b}-\mathrm{a}} ; \mathrm{a} < \mathrm{x} < \mathrm{b} \\& \mathrm{f}(\mathrm{x})=\frac{1}{10-1.5} ; 1.5 < \mathrm{x} < 10 \\& \mathrm{f}(\mathrm{x})=\frac{1}{8.5} \\& \begin{aligned}& \mathrm{P}(\mathrm{X} > 5)=\left(\frac{1}{8.5}\right)(10-5) \\&=\frac{5}{8.5} \\&=0.58823 \\&= 58.23 \%\end{aligned}\end{aligned}$

So, 58.23% percent of the problems take more than 300 seconds or 5 minutes to resolve.

(a) Percentage of problems take less than 300 seconds or 5 minutes = 100-58.23 =41.77%

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