Question

Assume that cans are filled so that the actual amounts have a mean of 16.00 ounces. A random sample of 36 cans has a mean amount of 16.71 ounces. The distribution of sample means of size 36 is normal with an assumed mean of 16.00 ounces and a standard deviation of 0.08 ounce.

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

Answer 1

Solution:- The sample mean 53.25 standard deviation from the mean of the distribution of sample​ means.

Mean = 16, S.D = 0.08, n = 36

x = 16.71

By applying normal distribution:-

$z = \frac{x-\mu }{\frac{\sigma }{\sqrt{n}}}$

z = 53.25