Solution Found!
The probability density function of the net weight in
Chapter 4, Problem 9E(choose chapter or problem)
Problem 9E
The probability density function of the net weight in pounds of a packaged chemical herbicide is f (x) = 2.0 for 49.75 < x < 50.25 pounds.
(a) Determine the probability that a package weighs more than 50 pounds.
(b) How much chemical is contained in 90% of all packages?
Questions & Answers
QUESTION:
Problem 9E
The probability density function of the net weight in pounds of a packaged chemical herbicide is f (x) = 2.0 for 49.75 < x < 50.25 pounds.
(a) Determine the probability that a package weighs more than 50 pounds.
(b) How much chemical is contained in 90% of all packages?
ANSWER:
Solution :
Step 1 of 2:
Given f (x) = 2.0 for 49.75 < x < 50.25 pounds.
Our goal is:
a). We need to find the probability that a package weighs more than 50 pounds.
b). We need to find How much chemical is contained in 90% of all packages.
a). The probability of more than 50 pounds.
Given P(X>50).
P(X>50) =
P(X>50) =
P(X>50) = 2(50.25)-2(50)
P(X>50) = 100.5-100
P(X>50) = 0.5
Therefore, P(X>50) = 0.5.