The time taken by a traditional nuclear reactor to generate one nuclear chain reaction with fast neutrons, \(X_{1}\), has mean 10 nanoseconds and variance 4 , while the time taken by an improved design of the reactor, \(X_{2}\), has mean 8 nanoseconds and variance 2.5. Find the expected time savings using the improved design when

(a) generating a single chain reaction;

(b) generating 5000 chain reactions.

(c) Find the standard deviation in part

(a) and (b), assuming all of the generating times are independent.