SOLUTION: 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

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Question 1204385: 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 49 and a standard deviation of 16. 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 by ikleyn(53937) About Me  (Show Source):
You can put this solution on YOUR website!
.

Probably, you mean making this computations using tables, but I think that the time to work
with tables gone into the past approximately 40 years ago.


I will work using calculators - regular TI-83/84 and/or online.


Regular calculators use a standard function 

    z-score = invNorm(area, mean, st.deviation),


where area is the area to the left of the z-score.  In our case

    z-score = invNorm(0.05, 49, 16) gives the answer  z-score = 22.682.


Online calculator  https://davidmlane.com/hyperstat/z_table.html  gives the same answer  
(use it in the "Value from an area" mode).


Rounded as requested, the answer is  score = 22.7.

Solved.