Suppose that an intelligence test is constructed to have a normal distribution with the mean of 100, and a standard deviation of 15.
i) Between what two scores symmetrically distributed around mean will 50% of people IQ scores have?
ii) Find out the interquartile range of this IQ score distribution.
iii) If 400 people were randomly selected, determine the probability that at least 315 people have IQ scores between 82.0 and 121.0.