Question

Question 23 1 pts The amount of time in hours that computers, produced by a manufacturer, functions before breaking down is a continuous random variable with probability density function given by f(x) = el=x/100/1001{>0}, where I{X>0} is 1 when X>0 and is otherwise. In a random sample of 1000 computers produced by the manufacturer, what is the probability that at least 600 of them function fewer than 100 hours? 0.9821 0.0179 0.4821

Answer 1

Given that amount of X has the P. d. f. given below

with f(x) = dende Solution - Given that amount of time (x) has the P. d. f. given below -%100 fli) = те 100 Comdicting We Set - 100 so , x has exponential distribution with parameta is 100 So, plac loo)=l-e loo [ .gf x~ Exp (1) F (Bel) E PLxzoj elnēts] len Soi 0.63212 the Probability that fewer than loo hows js P(x2100)co 6 3Q là Let y denotf sthe number of Computers take fewe 100 hours 1000x0 -68212 = than So, Ely)= 632.12 [ELY)=nb] S.D. = Unpa = 1000 to 163212 X0 1368 15.25

So Ply> 600 ) Р - Hz воо -") 6 зэ- 12 ) Pl2> Бое — боо - 39 1а 158 wholt 2 is (27 - - o6a ) Standard normal variate С. 988) |