Answer to Question #182505 in Statistics and Probability for Mitsss

Question

The average number of milligrams (mg) of cholesterol in a cup of a certain brand of ice cream is 660 mg, and the standard deviation is 35 mg. Assume that the variable is normally distributed. If a sample of 10 cups of ice cream is selected, what is the probability that the mean of the sample will be larger than 670 mg?

Answer 1

Solution:

Given, $\mu=660,\sigma=35,n=10$

$X\sim N(\mu,\sigma^2)$

Now, $P(X>670)=P(z>\dfrac{670-660}{35/\sqrt{10}})=P(z>0.9035)$

$=1-P(z\le0.9035)\approx1-0.81594=0.18403$