00:01
For this question, it stated that purchase amounts in a store are normally distributed with the mean of 200, a standard deviation of 70, and we take a sample of 100 purchases, and we're asked, what is the probability that the average purchase is less than 205? so this sample is going to have some sample average.
00:26
We want the probability that the sample average is smaller than 205.
00:32
And we can answer this question if we understand how x -var is distributed.
00:39
If we were to take sample after sample of size 100, the sample average would vary from sample to sample because it's a random sample.
00:47
That means that the sample average has some distribution.
00:52
Because the population is normally distributed, population of purchases or purchase prices, this means that the averages of samples drawn from this population are also normally distributed.
01:08
Furthermore, the mean of the sample means would be equal to the mean of the population, and the standard deviation of sample means is equal to the population standard deviation over the square rate of the sample size.
01:31
And this gives us 7...