Answer to Question #254564 in Statistics and Probability for mcm

Question

The time taken to complete a particular type of a job is distributed approximately normally with mean 1.8 and standard deviation of 0. 1hours.Calculate the estimated completion time (to the nearest minute) that should be set so that there is a 90% chance that the job is completed on time.

Answer 1

The distribution of the required time is $N(1.8, 0.1^{2}) = 1.8 + 0.1N(0,1)$

Our goal is to find such a value a, that: $P(1.8+0.1N(0,1) < a) = 0.9$

$P(N(0,1) < {\frac {a-1.8} {0.1}}) = 0.9$

So, ${\frac {a-1.8} {0.1}} = 1.28\to a = 1.928$ hours, or 115.68 minutes, or 116 if round to the nearest minute

116 minutes