IQs of Individuals Are Normally Distributed with a Mean of 100

Essay

IQs of individuals are normally distributed with a mean of 100 and a standard deviation
of 16.If you sampled students at your college and assumed, as the null hypothesis, that
they had the same IQ as the population, then in a random sample of size (a) $n = 25$ , find $\operatorname { Pr } ( \bar { Y } < 105 )$ .
(b) $n = 100$ , find $\operatorname { Pr } ( \bar { Y } > 97 )$ .
(c) $n = 144$ , find $\operatorname { Pr } ( 101 < \bar { Y } < 103 )$ .