Respuesta :
Answer:
a) 0.9917
b) 0.1652
Step-by-step explanation:
We are given the following in the question:
The time for repair follows an exponential distribution.
[tex]\lambda = 0.6[/tex]
a) P(repair takes less than 8 hours)
[tex]P(x\leq 8)\\=\displaystyle\int^8_0(0.6)e^{-0.6x}dx\\\\=\big[e^{-0.6x}\big]^8_0\\\\=-(e^{-0.6(8)}-e^{-0.6(0)})\\=0.9917[/tex]
0.9917 is the probability that a repair takes less than 8 hours.
b) the conditional probability that a repair takes at least 7 hours, given that it takes more than 4 hours
[tex]P(x\geq 7|x\geq 4) = \dfrac{P(x\geq 7)}{P(x\geq 4)}\\\\=\dfrac{1-\int^{7}_00.6e^{-0.6x}dx}{1-\int^{4}_00.6e^{-0.6x}dx}\\\\=\dfrac{1-(-e^{-0.6(7)}+e^{0})}{1-(-e^{-0.6(4)}+e^{0})}\\\\=0.1652[/tex]
thus, 0.1652 is the conditional probability that a repair takes at least 7 hours, given that it takes more than 4 hours.
