In a small town,there are 3,000 registered voters.An editor of a local newspaper would like to predict the outcome of the next election;in particular,he is interested in the likelihood that Eli Brady will be elected.The editor believes that Eli,a local hero,will garner 54% of the vote.A poll of 500 registered voters is taken.Assuming that the editor's belief is true,calculate: a.The expected value and the standard deviation (standard error)of the sample proportion.b.The probability that the sample proportion score is more than 0.58.
A random sample of nine cast aluminum pots is taken from a production line once every hour.The interior diameter of the pots is measured and the sample mean is calculated.The target for the diameter is 12 inches and the standard deviation for the pot diameter is 0.05 inches.Assume the pot diameter is normally distributed.a.Construct the centerline and the upper and lower control limits for the chart.b.The means of the samples for a given eight-hour day are 12.01 12.06 11.97 12.08 11.92 11.95 11.97 12.04.Plot these values on the chart.c.Does it appear that the process is under control? Explain.
In a recent investigation,the National Highway Traffic Safety Administration (NHTSA)found that the Chevrolet Volt and other electric vehicles do not pose a greater risk of fire than gasoline-powered vehicles (The Boston Globe,January 25,2012).Specifically,it was determined that "no discernible defect trend exists." Suppose a consumer advocacy group wants to verify some of these claims by constructing a chart.The group expects 2% of electric cars to catch fire each month.For each of the last six months,500 electric car owners are asked if their cars have caught fire.These sample proportions are obtained: 0.010 0.020 0.015 0.030 0.025 0.015.a.Assuming that the group expectation is correct,construct the centerline and the upper and lower control limits for the chart.b.Do the consumer group's findings support those of the NHTSA? Explain the answer.
A bottled water plant uses a production process designed to fill bottles with 20 ounces of water.The population of filling volumes is normally distributed with a standard deviation of 1.3 ounces.Periodically,process engineers take 20-bottle samples and compute the sample mean.
a.What are the upper and lower control limits? b.Suppose the last five sample means were 19.4 20.2 20.5 20.7 21.1 ounces.Is the process under control?