Question

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?

Answer 1

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

Explanation:

Z-score:

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

`Z = (X - \mu)/(s)`

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:

`X = 17.79, \mu = 17, s = 0.08`

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

`Z = (X - \mu)/(s)`

`Z = (17.79 - 17)/(0.08)`

`Z = 9.875`

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