-A manufacturing company has developed a fuel-efficient machine that combines pressure washing with steam cleaning. It is designed to deliver 7 gallons of cleaner per minute at 1,000 pounds per square inch for pressure washing. In fact, it delivers an amount at random anywhe petween 6.5 and 7.5 gallons per minute. Assume that y, the amount of cleaner delivered, is a uniform random variable with probability densit if 6.5 sys 7.5 elsewhere %3D 1. Find the mean and standard deviation of y. Graph fly), showing the locations of the mean, 1 and 2 standard deviation intervals around the mean. 2. Find the probability that more than 7.2 gallons of cleaner are dispensed per minute.

A First Course in Probability (10th Edition)
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ISBN:9780134753119
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Chapter1: Combinatorial Analysis
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Question 6. 1, 2. Please solve it step by step.
6)- A manufacturing company has developed a fuel-efficient machine that combines pressure washing with steam cleaning. It is designed to
deliver 7 gallons of cleaner per minute at 1,000 pounds per square inch for pressure washing. In fact, it delivers an amount at random anywhere
between 6.5 and 7.5 gallons per minute. Assume that y, the amount of cleaner delivered, is a uniform random variable with probability density
fG) = {o
if 6.5 <ys 7.5
elsewhere
1. Find the mean and standard deviation of y. Graph f(y), showing the locations of the mean, 1 and 2 standard deviation intervals around the
mean.
2. Find the probability that more than 7.2 gallons of cleaner are dispensed per minute.
Transcribed Image Text:6)- A manufacturing company has developed a fuel-efficient machine that combines pressure washing with steam cleaning. It is designed to deliver 7 gallons of cleaner per minute at 1,000 pounds per square inch for pressure washing. In fact, it delivers an amount at random anywhere between 6.5 and 7.5 gallons per minute. Assume that y, the amount of cleaner delivered, is a uniform random variable with probability density fG) = {o if 6.5 <ys 7.5 elsewhere 1. Find the mean and standard deviation of y. Graph f(y), showing the locations of the mean, 1 and 2 standard deviation intervals around the mean. 2. Find the probability that more than 7.2 gallons of cleaner are dispensed per minute.
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