00:01
Okay, so we're going to do 7 .87.
00:07
Now the time to process orders at the service counter of a pharmacy, this is exponentially distributed with mean 10.
00:16
So we're just going to denote t as the process time of the order.
00:31
And we know that t is exponentially distributed with mean 10.
00:37
So now we're going to denote ti by the process time for ith customer and we want to find the probability that the at least half of the customers need to wait more than 10 minutes.
01:09
So what we do is we define xi 1 if t i.
01:20
Is more than eot which is 10 and 0 otherwise now notice that by the way i goes from 1 through 100 because there are 100 customers now notice that xi follows vanuilly of p where is equal to the probability that time is more than 10.
02:16
And also the sum of xi, this follows, let's notice by the big x, this follows binomial of 100 np, where p is this one.
02:49
So now all we need to do is to find the probability of this sum is at least 500.
03:05
No, no, not 500, 50...