In: Statistics and Probability
Cans of regular Coke are labeled as containing 12 oz. Statistics students weighted the content of 8 randomly chosen cans, and found the mean weight to be 12.14. Assume that cans of Coke are filled so that the actual amounts are normally distributed with a mean of 12.00 oz and a standard deviation of 0.09 oz. Find the probability that a sample of 8 cans will have a mean amount of at least 12.14 oz.
Solution :
Given that ,
mean =
= 12
standard deviation =
= 0.09
n = 8
=
/
n = 0.09 /
8
P( 12.14) = 1 -
P(
12.14)
= 1 - P[(
-
) /
< (12.14 - 12) / 0.09 /
8 ]
= 1 - P(z < 4.40)
= 1 - 1
0
Probability = 0