Answer:
Probability that the lifetime of the machine part is less than 13 = 0.6782
Step-by-step explanation:
given that [tex]f(x)=(10+x)^{-2}[/tex]
Normalizing the function we get
[tex]\int_{0 }^{50}cf(x)dx=1[/tex]
[tex]\int_{0 }^{50}c(10+x)^{-2}dx=1[/tex]
[tex]\therefore a=\frac{1}{\int_{0 }^{50}(10+x)^{-2}dx}[/tex]
[tex]\therefore a=12[/tex]
[tex]P(x< 13)=\int_{0}^{13}12(10+x)^{-2}dx\\\\P(X< 13)=0.6782[/tex]
