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?

Tammy Todd

Tammy Todd

Answered question

2021-08-22

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 & Explanation

Maciej Morrow

Maciej Morrow

Skilled2021-08-23Added 98 answers

The probability densit y function f of the random variable X is given as:
f(x)=2,49.75

a) Straightforward calculation gives:
P(X>50)=50.25502dx=0.252=0.5
b) Write the equality:
0.9=P(X>x)=50.25x2dy=2(50.25x)
and solve for x:
x=49.8
Result: a)0.5 b)49.8

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