Question

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 12.13. 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 0.12 oz. Find the probability that a sample of 5 cans will have a mean amount of at least 12.13 oz.

Answer 1

Answer: 0.0078

Step-by-step explanation:

We 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 0.12 oz.

As per given , we have

$\mu=12.00\ oz$  and $\sigma=0.12\ oz$

Sample size : n= 5

Let $\overline{X}$ be the sample mean amount of coke in can.

Then, the  probability that a sample of 5 cans will have a mean amount of at least 12.13 oz will be :_

$P(\overline{x}\geq12.13)=1-P(\overline{x}$

$=1-P(z$

$= 1-0.9922=0.0078$  [By using z-table]

Hence, the required probability = 0.0078