00:01
This problem says a normally distributed population has a mean of 575 and a standard deviation of 45.
00:06
Determine the probability that a random sample of size 9 selected from this population will have a sample mean less than 549, and also determine the probability that a random sample of size 25 selected from the population will have a sample mean greater than or equal to 596.
00:20
And since we have a normally distributed population, we can treat our sampling distributions as normal as well, and that means we can find our probabilities using normal cdf in our calculator, which starts off needing the lower bound and upper bound that we want the probability between.
00:33
And here we want the probability that our sample mean will be less than 549, so that will be our upper bound.
00:39
And to make sure we include everything to the left for less than 549, we'll use negative infinity for the lower bound, and that's followed by the mean of our sampling distribution and standard deviation of the sample mean.
00:49
And the mean of our sampling distribution is equivalent to the mean of the population, so that says 575, but the standard of the sample mean is the standard deviation of the population divided by the square root of the sample size...