00:01
This problem says a random sample is drawn from a normally distributed population with a mean of 15 and a standard deviation of 1 .9.
00:07
And we are first asked, are the sampling distributions of the sample mean with n equals 23 and n equals 46 normally distributed? and if we weren't told that our population was normally distributed, the n equals 46 would be the only one that's normally distributed because that's the only one that's greater than or equal to 30, which means that would be the only one that has the central limit theorem that would apply because of the sample size.
00:28
But since our population was told to be normally distributed, that means both of these sample means will have a normal distribution because of that.
00:36
So our first choice would be correct there.
00:38
And then for b, we want to find the probability that for both of these samples that the sample mean would be less than 15 .9.
00:44
And since we can treat both of these sampling distributions as approximately normal because the population is normal, we can find our probability for both using normal cdf in our calculator.
00:53
And for normal cdf in your calculator, you need four values to find a probability.
00:56
And that starts with the lower bound and the upper bound that you want the probability between.
01:00
And here we want the probability that we're less than 15 .9, so that would be our upper bound...