The State Department of Weights and Measures is responsible for making sure that commercial weighing and measuring devices,such as scales,are accurate so customers and businesses are not cheated.Periodically,employees of the department go to businesses and test their scales.For example,a dairy bottles milk in 1-gallon containers.Suppose that if the filling process is working correctly,the mean volume of all gallon containers is 1.00 gallon with a standard deviation equal to 0.10 gallons.Based on this information,if the department employee selects a random sample of n = 9 containers,what is the probability that the mean volume for the sample will be greater than 1.01 gallons?
A)0.3821
B)0.1179
C)0.6179
D)0.2358

Question

Quizplus · Accepted Answer

The probability that the mean volume for the sample will be greater than 1.01 gallons is 0.3821. This is because the mean volume of all gallon containers is 1.00 gallon with a standard deviation equal to 0.10 gallons, and the sample size is 9. Therefore, the sampling distribution of the mean will have a mean of 1.00 gallon and a standard deviation of 0.10/sqrt(9) = 0.0333 gallons. The probability that the mean volume for the sample will be greater than 1.01 gallons is the area under the sampling distribution of the mean to the right of 1.01 gallons, which is 0.3821.

The State Department of Weights and Measures Is Responsible for Making