It Is Desired to Test $\mathrm { H } _ { 0 } : \mu = 50$

Multiple Choice

It is desired to test $\mathrm { H } _ { 0 } : \mu = 50$ against $\mathrm { H } _ { \mathrm { A } } : \mu \neq 50$ using $\alpha = 0.10$ . The population in question is uniformly distributed with a standard deviation of 15. A random sample of 49 will be drawn from this population. If $\mu$ is really equal to 48 , what is the probability that the hypothesis test would lead the investigator to commit a Type II error?

A) $0.2433$
B) $0.8994$
C) $0.7567$
D) $0.1006$