machine is set up so that the fill volume ollows a uniform distribution between

Question

machine is set up so that the fill volume ollows a uniform distribution between 11.94 and 12.06 ounces. a) Report the mean and the standard deviation of the amount of soft drink in a b) What is the probability that one randomly selected can contains the amount about to randomly select 36 can of soft drink within 0.01 ounces of the true mean? cans of a soft drink. What is the mean and the standard deviation of the average amountof o drink per can in a nndom sample of size 3097 d) What is the probability that the sample average amount of drink per can will be within 0.01 of the true mean?

Explanation / Answer

Mean = 1/2 (a+b) = 1/2(11.94+12.06) = 12 SD = 1/12 (b-a)^2 = 1/12(12.06-11.94)^2 = 0.0012

P(|X-mu|<0.01) = P(11.99<X<12.01) = (12.01-11.99)/(12.06-11.94) = 0.1667

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