Question

2. Boxes of sugar are filled by machine with considerable accuracy. The distribution of box weights is normal and has a mean of 32 ounces with a standard deviation of 2 ounces. A quality control inspector takes a sample of n=16 boxes and finds that the sample mean is 31 ounces of sugar. What is the probability of obtaining such a sample with this much shortchanging in its boxes? Should the inspector suspect that the filling machinery needs repair?

Answer 1

Given,

$\mu$ = 32 ounces, $\sigma$ = 2 ounces

Standard error of sample mean =
ulo
= 2 / $\sqrt{16}$ = 0.25

Probability of obtaining such a sample = P($\bar{X}$ < 31)

= P[Z < (31 - 32) / 0.25]

= P[Z < -4]

= 0.00003

Since the probability of obtaining such a sample is very low, when we assume that the population mean is 32 ounces, the inspector should suspect that the filling machinery is not accurate in filling 32 ounces of sugar and needs repair.