A company has designed the new braking system for electric powered automobiles. To measure the lifetime of system, the design engineers place the braking system on 50 electric powered cars and test them under simulated city driving. Let Yi be the time to failure of the braking system of the i th car. The failure times are recorded in units of 10,000 miles and assume that the distribution of the time to failure of the braking system is exponential with the mean value of 8 (80,000 miles).
Compute the mean and standard deviation of Ybar and using CLT, what is the probaility that the sample mean based upon 50 observations will determine the true mea of 8 in a margin of error of +-2.