Assume that cans are filled so that the actual amounts have a mean of 17.00 ounces. A random sample of 36 cans has a mean amount of 17.79 ounces. The distribution of sample means of size 36 is normal with an assumed mean of 17.00 ounces and a standard deviation of 0.08 ounce. Required:
How many standard deviations is the sample mean from the mean of the distribution of sample?

The sample mean is 9.875 standard deviations from the mean of the distribution of sample

Step-by-step explanation:

Z-score:

In a set with mean and standard deviation s, the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

How many standard deviations is the sample mean from the mean of the distribution of sample?

The sample mean is 9.875 standard deviations from the mean of the distribution of sample

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0