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A machine is set to pump cleanser into a process at the rate of 5 gallons...

A machine is set to pump cleanser into a process at the rate of 5 gallons per minute. Upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 5 to 9 gallons per minute. [Round to four decimal places]


What is the probability that the machine to pump more than 8.71 gallons per minute?

What is the probability that the machine to pump is within 1.6 standard deviation of mean?

Math   Statistics-And-Probability   
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Answer #1

We are given the distribution here as:

a) The probability that the machine to pump more than 8.71 gallons per minute here is computed as:

b) The mean and standard deviation here are computed as:

Now the probability that the machine to pump is within 1.6 standard deviation of mean is computed here as:

7 - 1.6*1.1547 = 5.15,
7 + 1.6*1.1547 = 8.85

Therefore the probability here is computed as:

Therefore 0.925 is the required probability here.

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