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The vending machine problem Have you ever purchased a hot drink from a vend- ing machine? The intended sequence of events runs something like this. You insert your money into the machine and select your preferred beverage. A cup falls out of the machine, landing upright. Liquid pours out until the cup is nearly full. You reach in, grab the piping hot cup, and drink happily. Sometimes, things go wrong. The machine might take your money and not give you anything in return. Or the cup might fall over. More fre- quently, everything goes smoothly until the liquid begins to flow. It might stop flowing when the cup is only half full. Or the liquid might keep coming until your cup overflows. Neither of these results leaves you satisfied. 2. 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. Explain to the company president why setting the machine's mean at 7.0 ounces might be smarter than setting it at 7.5 ounces. 3. Customers may be irritated if they get a cup with too little liquid from the machine. At what value The vending machine company wants to keep customers happy. 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 that is set in the machine. μ • σ = 0.2 ounces QUESTIONS 1. Suppose the company sets the machine's mean at μ = 7.5 ounces. What percent of cups would overflow? Show your work. 3.2 Normal Distributions 135 should the machine's mean be set to ensure that 90% of cups contain at least 7 ounces? 4. Given the issues raised in the previous two questions, what mean setting for the machine would you recommend? Write a brief report to the vending machine company president that explains your answer.

The vending machine problem Have you ever purchased a hot drink from a vend- ing machine? The intended sequence of events runs something like this. You insert your money into the machine and select your preferred beverage. A cup falls out of the machine, landing upright. Liquid pours out until the cup is nearly full. You reach in, grab the piping hot cup, and drink happily. Sometimes, things go wrong. The machine might take your money and not give you anything in return. Or the cup might fall over. More fre- quently, everything goes smoothly until the liquid begins to flow. It might stop flowing when the cup is only half full. Or the liquid might keep coming until your cup overflows. Neither of these results leaves you satisfied. 2. 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. Explain to the company president why setting the machine's mean at 7.0 ounces might be smarter than setting it at 7.5 ounces. 3. Customers may be irritated if they get a cup with too little liquid from the machine. At what value The vending machine company wants to keep customers happy. 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 that is set in the machine. μ • σ = 0.2 ounces QUESTIONS 1. Suppose the company sets the machine's mean at μ = 7.5 ounces. What percent of cups would overflow? Show your work. 3.2 Normal Distributions 135 should the machine's mean be set to ensure that 90% of cups contain at least 7 ounces? 4. Given the issues raised in the previous two questions, what mean setting for the machine would you recommend? Write a brief report to the vending machine company president that explains your answer.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The vending machine problem Have you ever purchased a hot drink from a vend- ing machine? The intended sequence of events runs something like this. You insert your money into the machine and select your preferred beverage. A cup falls out of the machine, landing upright. Liquid pours out until the cup is nearly full. You reach in, grab the piping hot cup, and drink happily. Sometimes, things go wrong. The machine might take your money and not give you anything in return. Or the cup might fall over. More fre- quently, everything goes smoothly until the liquid begins to flow. It might stop flowing when the cup is only half full. Or the liquid might keep coming until your cup overflows. Neither of these results leaves you satisfied. 2. 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. Explain to the company president why setting the machine's mean at 7.0 ounces might be smarter than setting it at 7.5 ounces. 3. Customers may be irritated if they get a cup with too little liquid from the machine. At what value APPLICATION 3.2 The vending machine company wants to keep customers happy. 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 that is set in the machine. σ= 0.2 ounces QUESTIONS 1. Suppose the company sets the machine's mean at μ = 7.5 ounces. What percent of cups would overflow? Show your work. 3.2 Normal Distributions 135 should the machine's mean be set to ensure that 90% of cups contain at least 7 ounces? 4. Given the issues raised in the previous two questions, what mean setting for the machine would you recommend? Write a brief report to the vending machine company president that explains your answer.
Transcribed Image Text:The vending machine problem Have you ever purchased a hot drink from a vend- ing machine? The intended sequence of events runs something like this. You insert your money into the machine and select your preferred beverage. A cup falls out of the machine, landing upright. Liquid pours out until the cup is nearly full. You reach in, grab the piping hot cup, and drink happily. Sometimes, things go wrong. The machine might take your money and not give you anything in return. Or the cup might fall over. More fre- quently, everything goes smoothly until the liquid begins to flow. It might stop flowing when the cup is only half full. Or the liquid might keep coming until your cup overflows. Neither of these results leaves you satisfied. 2. 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. Explain to the company president why setting the machine's mean at 7.0 ounces might be smarter than setting it at 7.5 ounces. 3. Customers may be irritated if they get a cup with too little liquid from the machine. At what value APPLICATION 3.2 The vending machine company wants to keep customers happy. 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 that is set in the machine. σ= 0.2 ounces QUESTIONS 1. Suppose the company sets the machine's mean at μ = 7.5 ounces. What percent of cups would overflow? Show your work. 3.2 Normal Distributions 135 should the machine's mean be set to ensure that 90% of cups contain at least 7 ounces? 4. Given the issues raised in the previous two questions, what mean setting for the machine would you recommend? Write a brief report to the vending machine company president that explains your answer.
Expert Solution
Step 1

This report is written to provide recommendations to the vending machine company president on the mean setting for the machine.

This report is based on the facts that the cups will hold 8 ounces and the amount of liquid dispensed varies according to a Normal distribution centred at the mean A that is set in the machine, sigma = 0.2 ounces.

The purpose of this report is to provide a solution that will ensure customer satisfaction when using the vending machine.

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