Question

3. A car dealer that sells 2000 vehicles provides a 4 years guarantee when buying a car, because it is known that the probability of getting a breakdown is only 0.1.

a) Find the probability that more than 1785 cars will not have any breakdown.

b) Find the expected number of non-breakdown cars

Answer 1

3)

Let X denote the number of cars the do not have a breakdown.

Then

Using Normal approximation,

a)

Required probability =

{Due to continuity correction as a result of using Normal approximation for Binomial distribution}

b)

Since

So,