An electric car manufacturer specifies that the car battery of their long range model has a capacity of 65 kilowatt-hours (kWh). They define the battery to be defective if the capacity is less than 64.5 kWh. Past experience suggests that the population mean battery capacity is 66.24 kWh with population standard deviation of 2.16kW. They are willing to assume that the battery capacities are normally distributed. It can also be assumed that the battery capacities of different cars are statistically independent.

(a) What is the probability that a particular battery is defective?

(b) The company quality control manager is confident that the assumption of normality of battery capacities is justified, because of the Central Limit Theorem. Is she correct?