Question

The lifetime of a machine part has a continuous distribution on the interval​ (0, 50​) with probability density function​ f, where​ f(x) is proportional to left parenthesis 10 plus x right parenthesis Superscript negative 2. Calculate the probability that the lifetime of the machine part is less than 13.

Answer 1

Answer:

Probability that the lifetime of the machine part is less than 13 = 0.6782

Step-by-step explanation:

given that $f(x)=(10+x)^{-2}$

Normalizing the function we get

$\int_{0 }^{50}cf(x)dx=1$

$\int_{0 }^{50}c(10+x)^{-2}dx=1$

$\therefore a=\frac{1}{\int_{0 }^{50}(10+x)^{-2}dx}$

$\therefore a=12$

$P(x< 13)=\int_{0}^{13}12(10+x)^{-2}dx\\\\P(X< 13)=0.6782$