In: Statistics and Probability
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
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