A factory uses a special kind of lubricant to maintain its four milling machines

Question

A factory uses a special kind of lubricant to maintain its four milling machines. The weekly lubricant usage for each machine can be approximated with a normal distribution. This distribution has a mean of 30 gallons and a standard deviation of 11.5 gallons, and it can be considered as an independent random variable (zero covariance, zero correlation) from machine to machine.

Suppose at the beginning of the week, the factory has a total of 150 gallons of lubricant in stock. The factory will not receive any replenishment of lubricant from its supplier until the end of the week.Assume that the total lubricant usage (four machines combined) also follows a normal distribution. What is the probability that the factory will run out of lubricant before the next replenishment arrives?

Explanation / Answer

Xi ~ N(30,11.5^2)

X1 + X2 + X3 + X4 ~ N(4*30 , 4 *11.5^2)

Y = X1 + X2 + X3 + X4

Y ~ N( 120,23^2)

Z = (Y - 120)/23

P(Y > 150 )

P(Z > (150 - 120)/23)

=P(Z > 1.30434782609)

=0.0961

Please rate my solution

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.