Question

on average, a certain kind of kitchen appliance requires repairs once every one years. assume that the times between repairs are exponentially distributed. what is the probability that the appliance will work at least eight years without requiring repairs?

Answer 1

We can use the exponential distribution formula to solve this problem:

P(X > 8) = e^(-λx)

where X is the time between repairs, λ is the rate parameter (1/1 = 1), and x is the time we are interested in (8 years).

P(X > 8) = e^(-1*8) = e^(-8) = 0.00033546

Therefore, the probability that the appliance will work at least eight years without requiring repairs is approximately 0.00033546, or about 0.0335%.