00:01
This problem says a random sample is drawn from a population with a mean of 70 and a standard deviation of 5 .8.
00:07
First we're asked, is the sampling distribution of the sample mean with n equals 17 and n equals 43 normally distributed? here, to have a normal distribution or approximately normal distribution for our sampling distribution, since we weren't told that our population was approximately normal, we would need a sample size that's greater than or equal to 30 for the central limit theorem to apply.
00:26
So, our sample of 43 would be approximately normal, but our sample of 17 would not be because it's not big enough.
00:32
And then, moving to b, we want the probability that the sample mean falls between 70 and 72 for our n equals 43 sample size.
00:40
And so, since we can approximate this as normal, we can find the probability using normal cdf in our calculator.
00:47
And for normal cdf in our calculator, we have to list four values to find the probability we're looking for.
00:52
Starting with the lower bound and the upper bound that we want the probability between...