Question

An entrepreneur produces headphones. For the Elite 75t model, the manufacturer guarantees a lifetime of at least 730 days. The entrepreneur knows that the lifetime of this model is normally distributed, with an average value for 730 days and a standard deviation of 20 days.

The manufacturer sells this model for 119.99 $. If the device survives two years, it will bring a profit of 19.99 $. Otherwise, the device will be replaced by the warranty and will result in a loss of 80 $.
a.) what is the probability that an Elite 75t will claim the warranty? Round to 4 decimals places.

b.) What is the probability that the manufacturer will not make a loss when selling 300 pieces?

C.) What assumptions have you made to answer the above questions?

Answer 1

The solution to this problem is given by