Question: I.Q. scores are normally distributed with mean 100 and standard deviation 15. Suppose \[X\]

denotes an I.Q. score. Find the following probabilities.

a) \[P\left( X\le 155 \right)\]

b) \[P\left( 92.5\le X\le 113.7 \right)\]

c) \[P\left( X\ge 117.5 \right)\]

e) The Smart People’s Club admits those whose I.Q. is in the top 2% of scores. What is the minimum score a person must attain to join the club?