Given that the volume of soda cans varies normally with mean of 12.0 fluid ounce

Question

Given that the volume of soda cans varies normally with mean of 12.0 fluid ounces and a known standard deviation of 1.0 fluid ounce; Find the probability of a soda can containing less than nine fluid ounces. Find the probability of a soda can containing more than eleven fluid ounces. Find the probability of a soda can containing between 11.5 and 12.5 fluid ounces. Find the probability of the mean volume of sixteen a soda cans to be between 11.5 and 12.5 fluid ounces. Assuming that an eight pack is rejected if the mean volume is in the bottom 7%, find this cut off volume, i.e. an upper limit. Construct a 94.2% confidence interval for the mean volume of nine soda cans measured at Jake's diner Emporium, given that the sample mean is 11.3 pounds.

Explanation / Answer

4) P(11.5 < X < 12.5) = P((11.5-12)/1 < Z < (12.5-12)/1) = P(Z < 0.5) - P(Z < -0.5) = 0.6915 - 0.3085 = 0.383

5) P(Z < z) = 0.07, z = -1.4758,
(x - 12)/1 = -1.4758, x = 13.48

6) significance level 0.058, n = 9, x = 11.3
zcrit = +/-1.9
94.2% CI = 11.3 +/- 1.9*(1/sqrt(9)) = (10.67, 11.93)

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