Question

At a fixed operating setting, the pressure in a line downstream of a reciprocating compressor has a mean value of 12.0 bar with a standard deviation of 1.0 bar based on a very large data set obtained from continuous monitoring.

Required:
What is the probability that the line pressure will exceed 13.0 bar during any measurement?

Answer 1

P [ Z > 13 ] = 0,1587 or P [ Z > 13 ] = 15,87 %

Explanation:

The probability that the line pressure will exceed 13.0 bar is:

P [ Z > 13 ] = 1 - P [ Z ≤ 13]

And P [ Z ≤ 13] will be find in z table for z (score) =

z ( score) = ( Z - μ₀ ) / σ

z (score) = (13 - 12 )/1

Then from z-table we find

P [ Z ≤ 13] = 0,8413

Finally

P [ Z > 13 ] = 1 - P [ Z ≤ 13]

P [ Z > 13 ] = 1 - 0,8413

P [ Z > 13 ] = 0,1587 or P [ Z > 13 ] = 15,87 %