Bottles of water are labeled as containing 12 oz. Statistics students weighted the content of 7 randomly chosen bottles and found the mean weight to be 12.15 oz.

Assume that bottles of water are filled so that the actual amounts are normally distributed with a mean of 12.00 oz. and a standard deviation of .09 oz. Find the probability that a sample of 7 cans will have a mean amount of at least 12.15 oz.

I took (12.15-12)/.09 and got 1.66666667. I took the value for 1.7 in the normal distribution table and got .9525. I entered that as my answer and it wasn't right, so I thought that maybe it was supposed to be 1-.9525, but that wasn't right either. Should the 7 cans somehow fit into this?

It's an online program that my homework is on, and it only tells you whether you're right or not. The more I thought about it, if the bottles have a mean of 12, they'll never have a mean of 12.15. I tried 0 and it came up correct.

I used this page

http://davidmlane.com/hyperstat/z_table.html
and got the same result as you did after
1 - .9525

What answer are you supposed to get?

To solve this problem, you are on the right track by converting the given mean and standard deviation into the standard normal distribution. The formula you used to calculate the z-score is correct.

However, since this question asks about the probability that a sample of 7 cans will have a mean amount of at least 12.15 oz, we need to take into account the sample size (n = 7) as well.

The formula to calculate the standard error (SE) of the sample mean is given by:

SE = standard deviation / sqrt(n)

In this case, the standard deviation is 0.09 oz and the sample size is 7. So, the SE = 0.09 / sqrt(7) ≈ 0.034 oz.

Now, to find the probability that a sample of 7 cans will have a mean amount of at least 12.15 oz, we need to find the area under the standard normal distribution curve to the right of the z-score you calculated (1.67 in this case).

Applying the z-table, you can find that the area to the right of 1.67 is approximately 0.0475. However, we need to convert this probability value to the area to the left of 1.67, which represents the probability of the mean being at least 12.15 oz. To do this, subtract the obtained value from 1:

Probability = 1 - 0.0475 = 0.9525

So, the correct probability that a sample of 7 bottles will have a mean amount of at least 12.15 oz is approximately 0.9525 (or 95.25%).

Therefore, the answer to the question is 0.9525 or 95.25%, assuming the actual amounts are normally distributed with a mean of 12.00 oz. and a standard deviation of 0.09 oz.