An aircrew escape systems are powered by a solid propellant. Specifications requires that the mean burning speed of this

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An aircrew escape systems are powered by a solid propellant.
Specifications requires that the mean burning
speed of this propellant is 50 cm/s (H0). It is known that the
standard deviation of burning speed is 2cm/s. An
inspector routinely check the quality from the will sample 25
propellant. The sample average burning speed will
be computed. If the sample average burning speed is smaller than
49.2 or great than 50.8, he will conclude that
the machine is not working properly.
(a) For H0: μ = 50 versus H1: μ 6= 50, find α.
(b) Find β if the true mean burning speed is 51.0.