Find the indicated probability or percentage for the sampling error.
-The amount of coffee that a filling machine puts into an 8-ounce jar is normally distributed with a mean of 8.2 ounces and a standard deviation of 0.18 ounce. Determine the percentage of samples of
Size 16 that will have mean amounts of coffee within 0.1 ounce of the population mean of 8.2
Ounces.
A)42.46%
B)97.36%
C)71.23%
D)98.68%

Question

Find the indicated probability or percentage for the sampling error.
-The amount of coffee that a filling machine puts into an 8-ounce jar is normally distributed with a mean of 8.2 ounces and a standard deviation of 0.18 ounce. Determine the percentage of samples of
Size 16 that will have mean amounts of coffee within 0.1 ounce of the population mean of 8.2
Ounces. 
A)42.46%
B)97.36%
C)71.23%
D)98.68%

Quizplus · Accepted Answer

The standard error of the mean is 0.18/sqrt(16) = 0.045 ounces. The probability of a sample mean being within 0.1 ounce of the population mean is the area under the normal curve between -0.1/0.045 = -2.22 and 0.1/0.045 = 2.22. This area is 0.9736, or 97.36%.

Find the Indicated Probability or Percentage for the Sampling Error