SOLUTION: Q-4: [5+3+5+5+2Marks] the American Association of Individual Investors publishes an annual guide to the top mutual funds. The table below contains the ratings of the total risk for

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: Q-4: [5+3+5+5+2Marks] the American Association of Individual Investors publishes an annual guide to the top mutual funds. The table below contains the ratings of the total risk for      Log On

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Question 1180232: Q-4: [5+3+5+5+2Marks] the American Association of Individual Investors publishes an annual guide to the top mutual funds. The table below contains the ratings of the total risk for 20 categories of mutual funds.
----------------------------------------------------------------------------------------------------
Total Risk:x |Low(1) | Below Average(2) | Average(3) | Above Average(4) | High(5)
-----------------------------|-------|------------------|------------|------------------|-----------
Number of fund categories | 6 | 3 | 2 | 3 | 6
-----------------------------|-------|------------------|------------|------------------|-----------
a) Construct a probability distribution table.
b) What are the expected value of total risk?
c) What is the standard deviation of total risk?
d) Determine the probability distribution function.
e) What is the probability that a total risk will be above 3?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
(a)
X p(X=x)
1 6/23
2 3/23
3 2/23
4 3/23
5 6/23

(b)

(c) , and in turn this gives
Var%28X%29+=+E%28X%5E2%29+-+%28E%28X%29%29%5E2+=+234%2F23+-+%2860%2F23%29%5E2+=+1782%2F529
SD%28X%29+=+sqrt%28Var%28X%29%29+=+sqrt%281782%2F529%29+=+1.8354 to 4 d.p.

(d) The probability mass function will be p%28x%29+=+%282%2B%28x-3%29%5E2%29%2F23, for x = 1, 2, 3, 4, 5. (This can be seen by observing the symmetry of values around x = 3.)

(e) P%28X+=+4%2C5%29+=+3%2F23+%2B+6%2F23+=+9%2F23