Question

The downtime per day for a certain computing facility averages 4 hours with a standard deviation of 0.8 hours. Which z-score would you use in order to find the probability that the total downtime for 35 days is less than 130.68 hours. Round the answer to two decimal places

Answer 1

Solution:

Given, the distribution with,

  $\mu$ = 4

$\sigma$ = 0.8

n = 35

To find total of these 35 days is less than 130.68

i.e. to find sample mean $\bar x$ is less than 130.68/35  

i.e. to find sample mean $\bar x$ is less than 3.73371428571

We know,

The sampling distribution of the $\bar x$ is approximately normal with

Mean $\mu_{\bar x}$ = $\mu$ = 4

SD $\sigma_{\bar x}$ =   
ulo
  = 0.8/$\sqrt{}$​35 =   0.13522468075

The required z score is

($\bar x$ - $\mu_{\bar x}$ )/$\sigma_{\bar x}$ = (3.73371428571 - 4)/0.13522468075 = -1.97

Answer : -1.97