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

Variance is
`1.514* 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} = (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 = (30000 - 25000)/(1.285)`

`\sigma = (5000)/(1.285) = 3891.051`

Variance,
`\sigma ^(2) = 3891.051^(2) = 1.514* 10^(7)`