A company has designed the new braking system for electric powered automobiles. To determine the lifetime of the system, the design engineers place the braking system on 50 electric powered cars as well as test them under simulated city driving. Let Yi be the time to failure of braking system of i th car. The failure times are recorded in units of 10,000 miles and suppose that the distribution of the time to failure of the braking system is exponential with a mean value of 8 (80,000 miles).
Let Y be the sample mean time to failure of the 50 cars.
What is the exact distribution of Y?, the mean of Y? the standard deviation of Y?