4. IQs of individuals are normally distributed with a mean of 100 and a standard deviation of 16. If you sample a group of students and assume, as the null hypothesis, that they have the same IQ as the population, then find the following probabilities on given samples: (n resembles the sample size) 2

a. n = 49, find Pr( < 105). (3 Marks)

b. n = 100, find Pr( > 97). (3 Marks)

c. n = 169, find Pr(101 < < 103). (4 Marks)