The exam scores on a certain Society of Actuaries (SOA) professonal examination are Normally distributed with a mean score of μ = 70% and a standard deviation of o = 5 %. (a) What is the probability that a random chosen person who is writing this SOA exam will score at most 65%? Note, when finding/using z-values, use three decimals. (use four decimals in your answer) (b) What proportion of all persons writing this SOA Exam will score between 74% and 83% on the exam? Use four decimals in your answer. (c) 34% of all persons writing this SOA Examination will not pass. What is the minimum mark needed to pass this exam? Enter your answer to two decimal places, and enter as a percentage. %

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