00:01
In this exercise we are told that shipment times are exponentially distributed with a mean time of 2 .16 days.
00:09
We consider a random sample of 70 shipments and we're asked to approximate the probability that the average shipping time is less than 1 .76 days.
00:20
So the sample of size 70 has some sample average time.
00:26
We want the probability that x -bar is less than 1 .76.
00:35
To answer this question we have to understand how x -bar is distributed.
00:38
Now since the sample size is large, it's greater than 30, the central limit theorem comes into play.
00:45
And this theorem tells us that for large sample sizes, sample means are approximately normally distributed regardless of the distribution of the population from which the samples are drawn.
01:06
Furthermore, the mean of sample means is equal to the mean of the population.
01:10
That's given to us in the question 2 .16.
01:14
And the standard deviation of sample means is equal to the population standard deviation over the square root of the sample size.
01:20
Now for an exponential random variable, standard deviation is equal to the mean.
01:29
So we have a standard deviation of 2 .16...