Question

In: Statistics and Probability

A machine pumps cleanser into a process at a rate of 7 gallons per minute.

A machine pumps cleanser into a process at a rate of 7 gallons per minute. Upon inspection, it is learned that the machine pumps cleanser at a rate described by the uniform distribution over the interval 6.5 to 7.5 gallons per minute.

a. What is the mean of this distribution? The standard deviation?

Answer: mean = 7, standard deviation = 0.29

b. Find the probability that the machine pumps less than 7 gallons during a randomly selected

minute.

Answer: 0.5

Solutions

Expert Solution

Given: A machine pumps cleanser into a process at a rate of 7 gallons per minute.

The machine pumps cleanser at a rate described by the uniform distribution over the interval 6.5 to 7.5 gallons per minute.

That is: X = The machine pumps cleanser follows a Uniform distribution (a=6.5 , b = 7.5)

Part a) What is the mean of this distribution? The standard deviation?

For Continuous Uniform distribution with parameters a and b, mean is given by:

Thus Mean = 7

and

standard deviation is given by:

(Rounded to two decimal places)

Part b) Find the probability that the machine pumps less than 7 gallons during a randomly selected minute.

P(X < 7) = ..........?

For Continuous Uniform distribution, cumulative distribution function is given:

Thus the probability that the machine pumps less than 7 gallons during a randomly selected minute is 0.5

orchestra answered 1 year ago

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