00:01
Consider x denotes time between arrivals of customers at the drive -up window of a bank, which follows exponential distribution with mean of 10 minutes.
00:25
The main value of exponential distribution can be obtained using the formula 1 by lambda.
00:33
Substituting the value of lambda here, we will get the main value as 0 .1.
00:41
In subpart a, we need to find probability that the arrival time between customers will be 7 minutes or less.
00:54
Note that the formula to find the cumulative probability of exponential random variable is 1 minus e power minus minus mu yx.
01:13
Applying this formula here it can be written as 1 minus e power minus 0 .1 into 7.
01:23
This is equal to 1 minus 0 .4 .000.
01:24
This is equal to 1 minus 0 .4.
01:28
49 -66 which is equal to 0 .5034.
01:36
Therefore the probability that the arrival time between customers will be 7 minutes or less is 0 .5034.
01:49
In subpart b, we need to find probability that the arrival time between customers will be between 3 and 7 minutes.
02:05
This can be written as probability of x less than or equal to 7 minus probability of x less than or equal to 3.
02:15
Applying the formula of cumulative probability of exponential distribution, this can be written as 1 minus 8 power minus 0 .1 into 7 minus 1 .1 into 7 minus 1 .1 .7 minus 1.
02:31
E power minus 0 .1 into 3...