Question

q3a:

Risk taare to new cutomers to measure their desire to take financial risks. The scores on the questionnai stomers, portfolio ma distributed with a important part of inves In order to make suitable investment decisions on behalf of their is approximately norm ques asure mean of 49 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. X
q3b:q3c:

Answer 1

a) P(X < x) = 0.05

Or, P((X - $\mu$)/$\sigma$ < (x - $\mu$)/$\sigma$) = 0.05

Or, P(Z < (x - 49)/14) = 0.05

Or, (x - 49)/14 = -1.645

Or, x = -1.645 * 14 + 49

Or, x = 26.0

b) At 95% confidence interval the critical value is z^* = 1.96

The 95% confidence interval is

$\bar x$ +/- z^* * $\sigma/\sqrt n$

= 33.3 +/- 1.96 * 23/$\sqrt 70$

= 33.3 +/- 5.4

= 27.9, 38.7

Lower limit = 27.9

Upper limit = 38.7

c) P(-1.8 < t < 1.8)

= P(t < 1.8) - P(t < -1.8)

= 0.9572 - 0.0428

= 0.9144

P(t > c) = 0.05

Or, P(t < c) = 0.95

Or, c = 1.740