Question

The exam scores on a certain Society of Actuaries (SOA) professional examination are Normally distributed with a mean score of μ=67% and a standard deviation of σ=5%.

(1 point) The exam scores on a certain Society of Actuaries (SOA) professonal examination are Normally distributed with a mean score of u = 67% 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 69%? 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 73% and 83% on the exam? Use four decimals in your answer. (C) 25% 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. O %

Answer 1

solution :- From the given data, - Here, u= 67% = 0.67 o = 6% = 0.05 a) 69% = 0.69. P(x50.69) 0.69 -0.67 0.05 - (Z < 0.4) 10.6554) (From z table! b) The scorre between 73% and 83% =) P (0.73 cxco.83) 73 0.67 x M 0.83 0.67) 0.05 0.05 = P(1. 2c z 3.2]

- Plzc 3.2) - Plzc1.2) - 0.9993 - 0.8849 - 0.1144 O. 1144 The a distribution of the 25% is P(222) = 25% Plzc2) = 0.25 Plzc.0.67) = 0.25 2 =-0.67 using z -scorre Forrmula, x=20 tu x = -0.67 x 0.05 + 0.67 x = 0.6365 x = 63.65%.
Thank you.