The widely used Stanford-Binet IQ test has a mean of 100 points and standard deviation of 15 points. Assume that the population of IQ scores on this test are normally distributed. a. The minimum score for entry into Mensa, a group for people with high IQs, is 138. Determine the proportion of this population who are eligible to join Mensa. b. Another high-IQ group known as the Triple Nine Society requires an IQ score at or above the 99.9th percentile, so that only the top 0.1% of IQ scores in the population are eligible. Determine the minimum IQ score required to join the Triple Nine Society. c. Marilyn vos Savant, author of the "Ask Marilyn" column in Parade magazine, is reported to have an IQ score of 228. How many standard deviations above the mean is this?