Question

An electric scooter manufacturer uses batteries that follow a normal distribution with a mean lifetime of 3 years and a standard deviation of 3 months. Is the manufacturer safe in providing a 4-year warranty on the batteries?

Answer 1

The lifetime of electric scooter follows a normal distribution with a mean lifetime of 3 years and standard deviation of 3 months.

X ~ (3, 3)

For X = 4,
z0 = (4 - 3)/3 = 1/3 = 0.33

Let's find: P(z < z0) = P(z < 0.33)
From the z-table,
= 0.6293

Hence, 62.93% of the electric scooters will have a lifetime of less than 3 years. Hence, there is a much probability that the scooters will be returned back to the manufacturer in the warranty period. Therefore, the manufacturer will be at risk of high losses due to the returns made. The manufacturer is not safe.