At a certain workstation in an assembly line, the time required to assemble a component is exponentially distributed with a mean time of 10 minutes.Find the probability that a component is assembled in 3 to 7 minutes?
A)0.5034
B)0.2592
C)0.2442
D)0.2942
E)0.5084

Question

Quizplus · Accepted Answer

The exponential distribution has a mean of 10 minutes, so the rate parameter λ is 1/10. The probability that a component is assembled in 3 to 7 minutes is the difference between the cumulative distribution function (CDF) values at 7 and 3 minutes: P(3 < X < 7) = F(7) - F(3) = (1 - e^(-7/10)) - (1 - e^(-3/10)) = e^(-3/10) - e^(-7/10) ≈ 0.2442.

At a Certain Workstation in an Assembly Line, the Time