00:01
We are told that the weights of catfish, we'll call that random variable x, are normally distributed with a mean of 3 .2 pounds and a standard deviation of 0 .8 pounds.
00:13
And we're asked what percentage of samples of 4 fish will have means between 3 and 4 pounds.
00:19
So we're taking samples of size 4.
00:23
Each sample is going to have some sample average.
00:28
What is the probability that the sample average is between 3 and 4? to answer this question, we need to understand how the sample averages would be distributed.
00:51
Since the samples come from a distribution that is normal, sample averages are also normally distributed.
01:01
Furthermore, the mean of sample averages is equal to the mean of the distribution from which they were drawn, which is 3 .2, and the standard deviation of the sample averages is equal to the population standard deviation.
01:20
By the square root of the sample size, which is .4.
01:33
So here we have completely defined the distribution of sample averages.
01:40
So now we can solve for this...