just Q4.. B and C Problem 4. (25 points) The length of satisfactory service (yea

Question

just Q4.. B and C

Problem 4. (25 points) The length of satisfactory service (yeaobability derns certain model ofiaptop computeris a randorn variable having actory service (years) provided bya f(x)-ke3 for xx0 0 for xs0 a) (10 points) Find the value of k that makes this a probabili ty density function .G , by (10 points) What is the 25th percentile for this distribution? (hint this is not a probability, rather an x value) For this problem just set it up and tell me how you would solve it. You don't need to calculate the actual value. k e x: in (o26) -26.2 6.25 / wit in 2.

Explanation / Answer

Q4 b) (1/4.5)* 0x e(-x/4.5) dx = 0.25

(1/4.5) * [-4.5 * e(-x/4.5) |0x ]= 0.25

-[e(-x/4.5) - 1] = 0.25

e(-x/4.5) = 0.75

-x/4.5 = ln(0.75)

x = 1.2946

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