Cans of regular Coke are labeled as containing 12 oz.
Statistics students weighted the content of 5 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 oz and a standard deviation of .1 oz. Find the probability that a sample of 5 cans will have a mean amount of at least 12.14 oz.
Statistics students weighted the content of 5 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 oz and a standard deviation of .1 oz. Find the probability that a sample of 5 cans will have a mean amount of at least 12.14 oz.
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for the sample mean of 5 cans mu = 12.0, sd = sigma/sqrt(5) = 0.04472
P(xbar>= 12.14) = P[(xbar-mu)/(sigma/√n) >= (12.14 - 12)/(0.1/√5) ] = P[ Z >= 3.130]
If your tables don't go up that far, you can say the probability is below that associated with the next smallest tabulated value.
The actual probability P[Z >= 3.13] = 0.000874
P(xbar>= 12.14) = P[(xbar-mu)/(sigma/√n) >= (12.14 - 12)/(0.1/√5) ] = P[ Z >= 3.130]
If your tables don't go up that far, you can say the probability is below that associated with the next smallest tabulated value.
The actual probability P[Z >= 3.13] = 0.000874