8.69 Two distinct solid fuel propellants, type A and type B, are being considered for a space program activity.

Burning rates of the propellant are crucial. Random samples of 20 specimens of the two propellants are taken with sample means 20.5 cm/sec for propellant A and 24.50 cm/sec for propellant B. It is generally assumed that the variability in burning rate is roughly the same for the two propellants and is given by a population standard deviation of 5 cm/sec. Assume that the burning rates for each propellant are approximately normal and hence make use of the Central Limit Theorem. Nothing is known about the two population mean burning rates, and it is hoped that this experiment might shed some light on them.

(a) If, indeed, μA = μB, what is P(¯XB − ¯XA ≥ 4.0)?

(b) Use your answer in

(a) to shed some light on the proposition that μA = μB .