Exam 7: Introduction to Sampling Distributions

Assume that n = 18 people are asked a yes/no survey question,and 6 people say "yes" while 12 people say "no." Based on this information the sample proportion can be assumed normally distributed.

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.The department's test process requires that they select a random sample of n = 9 containers.If the sample mean is less than 0.97 gallons,the department will fine the dairy.Based on this information,what is the probability that the dairy will get fined even when its filling process is working correctly?

The Fallbrook Distributing Company has a soft drink bottling plant in Plano,Texas.Based on historical records,if its filling machine is working properly,the mean fill volume per can is 12.0 ounces with a standard deviation equal to 0.13 ounces.Further,the distribution of fill amounts is known to be normally distributed.The State of Texas has a department whose job it is to check on such consumer-related processes as soft drink filling.The idea is to protect the consumer.The department arrives at the Fallbrook plant once a month on an unscheduled day.When they arrive,they randomly select n = 4 cans and carefully measure the volume in each can.If any of these cans contains less than 11.85 ounces,the plant is shut down until a full inspection of the filling process is performed.Based on this information,the probability that the plant will get shut down if it is operating properly is approximately 0.4141.

The J.R.Simplot Company produces frozen French fries that are then sold to customers such as McDonald's.The "prime" line of fries has an average length of 6.00 inches with a standard deviation of 0.50 inches.To make sure that Simplot continues to meet the quality standard for "prime" fries,they plan to select a random sample of n = 100 fries each day.Yesterday,the sample mean was 6.05 inches.What is the probability that the mean would be 6.05 inches or more if they are meeting the quality standards?