Dr. Eliplim Agbenoxevi works in the Quality Control Department of a large Information

Technology company in Ghana. The time, T minutes, it takes him to analyse a sample is

normally distributed with mean 18 minutes and standard deviation 5 minutes.

(a) Find the probability that he takes longer than 20 minutes to analyse the next sample

The Information Technology company has a large store of samples analysed by Dr. Eliplim

Agbenoxevi with the time taken for each analysis recorded. Another staff by name Dr. Akuvi

Wolekplimeis investigating the samples that took her colleague longer than 15 minutes to

analyse. She selects, at random, one of the samples that took Dr. Eliplim Agbenoxevi longer

than 15 minutes to analyse.

(b) Find the probability that this sample took Dr. Akuvi Wolekplime more than 20 minutes

to analyse, given that it took her colleague more than 15 minutes to analyse?