Unlike the traditional IQ test, a group of researchers have designed new IQ questions
testing for the 9 different types of intelligence. The distribution of IQ scores using the new test for high
school students is normally distributed with a mean of 80 points and a standard deviation of 12 points.
Use technology to find the following. (Note: for full credit, write correct probability notation)
(a) Find the probability to 3 decimal places that a high school student chosen at random has an IQ
score between 60 to 75 points, inclusive.
(b) A student will need special attention if the student’s IQ score is below 55 (at most 54) or above
100 (at least 101). What proportion of the high school students will need special attention?
Hint: Look carefully at the bolded phrases.
(c) Mensa International is the largest and oldest high IQ society in the world. Members of this
society are individuals who score at the 98th percentile or higher on this new IQ test. Determine the
cutoff IQ score (it must be a whole number) to be a member of Mensa International.
