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A vending machine company wants to keep customers satisfied yet safe. So they have decided to hire you as a statistical consultant. They provide you with the following summary of important facts about the vending machine:
-Cups will hold 8 ounces.
-The amount of liquid dispensed varies according to a Normal distribution centered at the mean μ that is set in the machine.
-σ = 0.2 ounces1) If a cup contains too much liquid, a customer may get burned from a spill. This could result in an expensive lawsuit for the company. Use your stats knowledge to calculate why setting the machine's mean at 7.0 ounces might be smarter than setting it at 7.5 ounces
2) Customers may be irritated if they get a cup with too little liquid from the machine. At what value (to the hundredth) should the machine's mean be set to ensure that 90% of cups contain at least 7 ounces?
3) Given the issues raised in the previous 2 questions (overflowing/burning & underfilling/unsatisfied), what mean setting for the machine would you recommend? You should not be using the same mean values as the previous 2 questions, show your calculations.
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