The lifetime of a stereo component is exponentially distributed with mean 1,000 days. What is the probability that the lifetime is greater than or equal to 700 days?

0.4966

Explanation:

For an exponentially distributed probability;

X = 700

The mean m = 1/h

Mean m = 1000

h = 1/1000 = 0.001

For,

The probability that the lifetime is greater than or equal to 700 days

P (x>700) = integral (upper limit infinite, lower limit 700) {h*exp (-hx) }dx

P (x>700) = 0 - (-exp (-h*700)) = exp (-0.001*700) = exp (-0.7) = 0.4966

Therefore the probability that the lifetime is greater than or equal to 700 days is 0.4966