Answer to Question #173059 in Statistics and Probability for Johb

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.

Given that ‘’normal-time’’ work ends at 6pm and a job is started at 4.00pm, determine the probability that the job will need overtime.                         (2marks)

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.                 (3marks)

 

Answer 1

Given $\mu=1.8, \sigma=0.1$

$$P(X>2)=1-P(X\leq2)$$

$$=1-P(Z\leq\dfrac{2-1.8}{0.1})=1-P(Z\leq2)$$

$$\approx0.02275$$

$$P(X<x)=P(Z<\dfrac{x-1.8}{0.1})=0.9$$

$$\dfrac{x-1.8}{0.1}\approx1.645$$

$$x=1hr\ 58\ min$$

The estimated completion time is 5.58 pm.