00:01
Given that the average speed driven on a highway is 58 .2 mph, the population standard deviation is 6 .9 mph, and we are asked what is the probability that a sample of 30 drivers will have a sample mean speed less than 57 mph.
00:23
We would have a random sample of 30 drivers and they would have some sample mean speed.
00:32
We want the probability that the sample mean is smaller than 57.
00:37
To answer this we have to understand how sample means would be distributed.
00:45
So for a random sample to a random sample of size 30, we would get different sample means.
00:51
This means that sample means have some distribution.
00:54
It's called the sampling distribution of sample means.
00:57
When the sample size is large, such as 30 or bigger, the central limit theorem comes into play, which tells us that the sample means are approximately normally distributed.
01:17
Furthermore, the mean of sample means, or the mean of the sampling distribution of sample means, is equal to the population mean, which is 58 .2, and the standard deviation of sample means is the population standard deviation over the square root of the sample size...