The Normal Distribution

Make sure you answer all questions in context and print out any outputs and graphs that you perform in RStudio. These printouts will serve as justification for your work. For ALL probabilities round your answers to 4 decimal places. When computing probabilities, please include an RStudio plot for the Normal distribution.

Introduction:

(Part I)Beverage cans can be made from a very thin sheet of aluminum, only 1/8 inch thick. Yet they must withstand pressure up to 90 lbs/in²(approximately 3 times the pressure of an automobile tire). Beverage companies often purchase can in large shipments. To ensure that can failures are rare, quality control inspectors sample several cans from each shipment and test their strength by placing them in testing machines that apply force until the can fails (is punctured or crushed). The testing process destroys the cans, so there's a limited number of cans tested.

Assume that a can is considered defective if it fails at a pressure of 90 lbs/in²or less. The quality control inspectors want the proportion of defective cans to be no more than 0.001, or 1 in 1000. They test 10 cans, with the following results: