Question

"Ali has 100 jobs that he must do in sequence, with the times required to do each of these jobs being independent random variables with mean 2.3 minutes and standard deviation 3.7 minutes. Aysun has 200 jobs that she must do in sequence, with the times required to do each of these jobs being independent random variables with mean 1.4 minutes and standard deviation 3.1 minutes. Note that the time required for Ali to do any of his jobs is independent from the time required for Aysun to do any of her jobs. Find the probability that Ali finishes before Aysun. Note that you just need to get an approximate probability using Central Limit Theorem."

Answer 1

Let X denote the time in minutes that Ali requires to finish 100 jobs,

The mean and standard deviation of X respectively is 230 minute and 37

Let Y denote the time in minutes that Aysun requires to finish 200 jobs,

The mean and standard deviation of Y respectively is 280 minute and 43.84

Then,

The difference will follow normal distribution with mean and standard deviation

Then define the standard random variable Z as

Hence the required probability is