10 An investment strategy has an expected return of 14 perce

(10)

An investment strategy has an expected return of 14 percent and a standard deviation of 8 percent. Assume investment returns are bell shaped.

How likely is it to earn a return between 6 percent and 22 percent? (Enter your response as decimal values (not percentages) rounded to 2 decimal places.)

How likely is it to earn a return greater than 22 percent?(Enter your response as decimal values (not percentages) rounded to 2 decimal places.)

How likely is it to earn a return below ?2 percent?(Enter your response as decimal values (not percentages) rounded to 2 decimal places.)

Solution

(a) P(6<X<22) = P((6-14)/8<(X-mean)/s <(22-14)/8)

=P(-1<Z<1)

=0.68 (from standard normal table)

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(b) P(X>22) = P(Z>1) =0.16 (from standard normal table)

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(c) P(X<-2) = P(Z<(-2-14)/8)

=P(Z<-2) =0.02(from standard normal table)