Answer to Question #320884 in Statistics and Probability for Nellie

Question

A food manufacturing company produces oatmeal cookies that have a sugar content that

is approximately normally distributed. The mean sugar content is 1.1 grams with a standard

deviation of 0.15 gram. Determine the probability that a random sample of 10 oatmeal cookies

will have an average sugar content of greater than 1.2 grams.

Answer 1

We have a normal distribution, $\mu=1.1, \sigma=0.15, n=10.$

Let's convert it to the standard normal distribution,

$z=\cfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\cfrac{1.2-1.1}{0.15/\sqrt{10}}=2.11,$

$P(\bar{X}>1.2)=1-P(\bar{X}<1.2)=\\ =1-P(Z<2.11)=$

$=1-0.9826=0.0174$ ​(from z-table).