Question

On average, a certain kind of kitchen appliance requires repairs once every four years. Assume that the times between repairs are exponentially distributed. What is the probability that the appliance will work no more than three years without requiring repairs?

Answer 1

X ~ Eponential ( $\lambda$ )

Where $\lambda$ = 1 / 4

We have to calculate P( X <= 3) = ?

P( X <= x) = e^{- $\lambda$ X}

So,

P( no more than 3 years without requiring repair) = 1 - e^-3/4

= 1- 0.4724

= 0.5276