Answer to Question #320884 in Statistics and Probability for Nellie

Question #320884

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.

1
Expert's answer
2022-03-31T07:47:19-0400

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

Let's convert it to the standard normal distribution,

z=xˉμσ/n=1.21.10.15/10=2.11,z=\cfrac{\bar{x}-\mu}{\sigma/\sqrt{n}}=\cfrac{1.2-1.1}{0.15/\sqrt{10}}=2.11,

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

=10.9826=0.0174=1-0.9826=0.0174 ​(from z-table).


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