Question

In an industrial​ setting, process steam has been found to be normally distributed with an average value of 25,000 pounds per hour. There is​ a(n) 80​% probability that steam flow lies between 20,000 and 30,000 pounds per hour. What is the variance of the steam​ flow?

Answer 1

Answer:

Variance is $1.514\times 10^{7}$

Solution:

As per the question:

Average value of the steam, $\mu$ = 25000 pounds per hour,

To calculate the variance, $\sigma ^{2}$ of the steam:

$\bar{Z} = \frac{x - \mu }{\sigma }$

where

$\sigma$ = standard deviation

$\bar{Z}$ at 0.8 is 1.285 from Z-table

Thus

$\sigma = \frac{x - \mu }{\bar{Z}}$

$\sigma = \frac{30000 - 25000}{1.285}$

$\sigma = \frac{5000}{1.285} = 3891.051$

Variance, $\sigma ^{2} = 3891.051^{2} = 1.514\times 10^{7}$