Question

A man has four (4) stock investments that have values: X1, X2, X3 and X4 where Xi ∼ N($5000, 2500) for i = 1, 2, 3, 4. Determine the probability that he sells all four investments on a given day if he has given an order to sell all four investments when: a.at least one of the four investments exceeds $5022 in value, b.all of the four investments exceeds $5022 in value, c.the average of all four of the investments exceeds $5022 in value.

Answer 1

P(X > 5022)

= P((X - )/ > (5022 - )/ )

= P(Z > (5022 - 5000)/50)

= P(Z > 0.44)

= 1 - P(Z < 0.44)

= 1 - 0.6700

= 0.33

a) n = 4

p = 0.33

It is a binomial distribution.

P(X = x) = nCx * p^x * (1 - p)^{n - x}

P(X > 1) = 1 - P(X < 1)

              = 1 - P(X = 0)

             = 1 - (4C0 * (0.33)^0 * (0.67)^4)

            = 1 - 0.2015 = 0.7985

b) P(X = 4) = 4C4 * (0.33)^4 * (0.67)^0 = 0.0119

c) P( > 5022)

= P(()/() > (5022 - )/( ))

= P(Z > (5022 - 5000)/(50/))

= P(Z > 0.88)

= 1 - P(Z < 0.88)

= 1 - 0.8106

= 0.1894