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.
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)=\\\\\n=1-P(Z<2.11)="
"=1-0.9826=0.0174" (from z-table).
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