Question

You are supervising annual testing of pressure relief valves at the Longhorn Refinery. Last year's results are given below. Of the X valves tested, Y valves needed maintenance work, and of the Y valves maintained, Z valves needed parts replaced. Please use last year's results to predict this year's probable results. See Assignment for dataset to use Y Needed Maintenance Z Needed Parts Replaced 10 20 30 X Valves Tested A 20 B)| 40 C 60 10 15

use data set B

Answer 1

The probability that the valve will need adjustment is 0.5

The probability that the valve under maintenance need adjustment is 0.5

hence the probability that valve will need adjustment is 0.5*0.5=.25

The probability that exactly less than 3 out of 10 valves will need adjustment is

$P(X<3)=\sum_{x=0}^{2}_{x=0}^{10}\textrm{C}(0.25)^x(1-0.25)^{10-x}=0.5256$