Question

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. What is P(X>50)

Answer 1

Answer:

$P(X>50)=0.5$

Step-by-step explanation:

The probability density function,$f(x)$, of a random variable X is defined as:-

$\int\limits^a_b {x} \, dx$=$\int\limits^{50.25}_{49.75} {2} \, dx$

To obtain P(X>50), we will integrate the function over the limits 50.25 and 50.0 as below:

$\int\limits^{50.25}_{50.00} {2} \, dx \\=0.25*2\\=0.5$

Therefore, P(x>50) is true for any value of x that is greater than 50 and therefore P(X>50)=0.5