Time between failures of a critical machine follow normal distribution, with a mean of 30 hours and standard deviation of 5 hours. If the random normal deviate chosen from a table of normally distributed random numbers is 2.5 , the number of simulated hours before the next failure will be:
A) 17.5
B) 32.5
C) 27.5
D) 42.5

Question

Quizplus · Accepted Answer

The number of simulated hours before the next failure can be calculated using the formula: $ \text{Simulated value} = \mu + Z\sigma $, where $ \mu $ is the mean, $ Z $ is the random normal deviate, and $ \sigma $ is the standard deviation. Substituting the given values: $ 30 + 2.5 \times 5 = 30 + 12.5 = 42.5 $ hours.

Time Between Failures of a Critical Machine Follow Normal Distribution