Question: The muzzle velocity of a projectile follows normal distribution with a standard deviation of 121 fps. The manufacturer of this projectile claims that the (population) mean muzzle velocity is greater than 3000 fps. A random sample of 25 projectiles yielded a sample mean (muzzle velocity) of 3040 fps.

(a) Test at a = 0.10 level, whether the manufacturer's claim is true.

(b) What is the P value?

(c) What is the probability of Type II Error ( \(\beta \) ), if the true (population) mean muzzle velocity is 3020 fps?