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A certain piece of machinery is known to fail according to a Poisson process.
a) In a series of tests, the piece was let operate till failure, repaired immediately, and let operate till next failure and so on for 3 months. The total number failures observed were 3. If the intent of the test was to determine , was the test run for too long, too short or just about the appropriate length of time ?
b) To minimize unscheduled shutdowns, the piece of machinery is to be inspected and maintained on a regular interval of X days. What X should you select to have 90% confidence that you will not see failures during operation?
c) Based on the results from (b), estimate the likelihood of finding no failure in 2 consecutive time periods.
d) Based on your results from (a) assign a probability distribution to  and update it by taking to account that you found no unscheduled shutdowns, under the maintenance schedule you found in (b) for 3 months.
A biologist has found the average weight of 12 randomly selected mud turtles to be 8.7 lb with standard deviation 3.6 lb. find a 90% confidence interval for the population mean weight of all such turtles.
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A safety engineer claims that only 40% of all workers wear safety helmets when they eat lunch at the workplace. Assuming that his claim is right, find the probability that at most 4 out of 6 workers randomly chosen will be wearing their helmets wh..
Give an example of how Regression Analysis can be used in your work to make a business decision. Give the dependent and independent variables.
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Construct a 99% confidence interval estimate of the population mean amount of paint in a 1-gallon can.
Following is based on information from Statistical abstract of the United States, Dec, 1992. Are A and B mutually exclusive?
Someone gives you 10 to 1 odds that you cannot roll a double number with the roll of a pair of dice. You win $10 if you succeed and you lose $1 if you fail. What is the expected value of the game for you? What can be expected if you play 100 times..
Determine the mean annual amount spent on household consumption per family with a sample of 100 families, an average amount of $8,000 spent, and if the population standard deviation is $500,
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