Answer to Question #198942 in Statistics and Probability for Jeng

Question

The average number of milligrams of cholesterol in a cup of a certain brand of milk tea is 500 mg, and the standard deviation is 30 mg. Assume that the data is normally the data is normally distributed.

A. If the 30 cups of milk tea are randomly selected, what is the probability that the cholesterol content Will be less than 510mg?

B. If the 30 cups of milk tea are randomly selected, what is the probability that the cholesterol content Will be grater than 510mg?

Answer 1

$\mu=500 \\ \sigma=30 \\ n = 30$

A.

$P(\bar{X}<510) = P(Z< \frac{\bar{X}- \mu}{\sigma / \sqrt{n}}) \\ = P(Z< \frac{510-500}{30/ \sqrt{30}}) \\ = P(Z<1.83) \\ = 0.9664$

B.

$P(\bar{X}>510) = 1 -P(\bar{X}<510) \\ = 1 -0.9664 \\ = 0.0336$