Question

Suppose a population has a mean of 400 and a standard deviation of 24. if a random sample of size 144 is drawn from the population, the probability of drawing a sample with a mean of more than 404.5 is:

Answer 1

Find the critical value or test statistic.
$z = \frac{m - \mu}{\sigma/\sqrt{n}} = \frac{404.5 - 400}{24/\sqrt{144}} = \frac{4.5}{2} = 2.25$

Find P(z > 2.25) using a normal distribution table

P(z > 2.25) = 0.0122