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In: Statistics and Probability

A shower head pumps water into a process at the rate of 5 gallons per minute....

A shower head pumps water into a process at the rate of 5 gallons per minute. Upon inspection, it is learned that the shower head pumps at a rate described by the uniform distribution over the interval 4 to 6 gallons per minutes.

a. Find the variance of the distribution. variance= 0.333 ?

b. Find the mean of the distribution. mean= 5

c. What proportion of the time does the machine pump more than 6.5 gallons per minute?

d. Would you expect the machine to pump more than 5.48 gallons per minute? Explain your answer.

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