Answer to Question #342954 in Statistics and Probability for yaoo

Question

The time taken to complete a particular type of job is distributed approximately normally with mean 1.8 hours and standard deviation 0.1 hours. (a) If normal-time work finishes at 6.00 p.m. and a job is started at 4.00 p.m., what is the probability that the job will need overtime payments? (b) What estimated completion time (to the nearest minute) should be set so that there is a 90% chance that the job is completed on time?

Answer 1

Given $\mu=1.8, \sigma=0.1$

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

$$=1-P(Z\leq2)\approx0.02275$$

$$P(X<x)=P(Z<\dfrac{x-1.8}{0.1})=0.9$$ $$\dfrac{x-1.8}{0.1}\approx1.6449$$ $$x=1.8+0.16449$$

$$x=1.96449\ h$$

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

The estimated completion time is 5.58 pm.