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You make cookies to sell that have a mean average of 10 chocolate chips per cookie with...

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topgun13 | (Level 2) Honors

Posted December 19, 2012 at 1:21 AM via web

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You make cookies to sell that have a mean average of 10 chocolate chips per cookie with a standard deviation of 2 chocolate chips. You bake cookies...

in normally distributed batches of 35. How likely is it to find a randomly chosen cookie that has 7 or less chocolate chips from your last batch of cookies?

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted December 19, 2012 at 1:57 AM (Answer #1)

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Given `mu=10,sigma=2,n=35` :

Find the probability that a randomly selected cookie has fewer than 7 chips.

First we make an adjustment to account for the fact that the number of chips is discrete, while the normal distribution is continuous.

P(x<7)==>P(x<6.5)

Now convert 6.5 to a z-score:

`z=(6.5-10)/2=-1.75`

Then P(x<6.5)=P(z<-1.75) Consulting a standard notrmal table or a calculator we find P(z<-1.75) is approximately 0.0401

The probability of a randomly selected cookie having fewer than 7 chips is approximately 4%.

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