If IQ scores are normally distributed with mean of 100 and standard deviation of 15.
(a) Determine the probability that randomly chosen person has an IQ score between 88 and 115. (Show work and round the answer to 4 decimal places)
(b) If 100 people are randomly chosen, determine the standard deviation of the sample mean IQ score. (Show work and round the answer to 2 decimal places)
(c) If 100 people are randomly selected, determine the probability that sample mean IQ score is greater than 97. (Show work and round the answer to 4 decimal places)