SOLUTION: suppose the mean weight of 32 ounce box of cereal is normally distributed with a mean of 32.2 ounces and standard deviation of 0.1 ounces. A) what percentage of boxes will weigh

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Question 1010875: suppose the mean weight of 32 ounce box of cereal is normally distributed with a mean of 32.2 ounces and standard deviation of 0.1 ounces.
A) what percentage of boxes will weigh more than 32.0 ounces, more than 32.2 ounces and between 31.0 and 32.2 ounces?
b) if one took random sample of 9 from these cereal boxes, what is the probability that the mean weight of nine sampled boxes would weigh less that 32.0 ounces
Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website!
mean 32.2
sd=0.1
z for 32 oz=(32-32.2)/0.1=-0.2/0.1=-2
It is the probability the z score is >=-2 or 0.9772
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More than 32.2 oz is 50%
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Between 31.0 and 32.2 ounces is
a z-score of -12 and a z-score of 0. That is 50% as well.
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z-score here is (32.0-32.2)/0.1/sqrt (9)
That is 3(-2)=-6 and the probability is essentially zero.