Question

BONUS The time it takes a worker on an assembly line to complete a task is exponentially distributed with a mean of 7.8 minutes. What is the probability that it will take a worker less than 5 minutes to complete the task? What is the probability that it will take a worker between 4 and 11 minutes to complete the task? What is the probability that it will take a worker greater than 7.5 minutes to complete the task? a. b. c. 3,4, 3 m

Answer 1

here this is exponential distriution with mean $\beta$ =7.8

a)

P(it takes less than 5 minutes)=P(X<5)=1-e^{-x/ $\beta$} =1-e^-5/7.8 =0.4732

b)

P(4<X<11)=P(X<11)-P(X<4)=(1-e^-11/7.8 )-(1-e^-4/7.8)=0.3547

c)

P(X>7.5)=1-P(X<7.5)=1-(1-e^-7.5/7.8)=0.3823