Question

Risk taking is an important part of investing. In order to make suitable investment decisions on behalf of their customers, portfolio managers give a questionnaire to new customers to measure their desire to take financial risks. The scores on the questionnaire are approximately normally distributed with a mean of 50 and a standard deviation of 14. The customers with scores in the bottom 5% are described as "risk averse." What is the questionnaire score that separates customers who are considered risk averse from those who are not? Carry your intermediate computations to at least four decimal places. Round your answer to one decimal place.

Answer 1

Given ,

= 50 , = 14

We convert this to standard normal as

P( X < x) = P( Z < x - / )

We have to calculate x such that

P( X < x) = 0.05

That is

P( Z < x - / ) = 0.05

From Z table, z-score for the probability of 0.05 is -1.6449

So,

x - / = -1.6449

Put values of and in above equation and solve for x

x - 50 / 14 = -1.6449

x = 27.0