Question

The historical returns on a balanced portfolio have had an average return of 14% and a standard deviation of 8%. Assume that returns on this portfolio follow a normal distribution. [You may find it useful to reference the z table.] a. What percentage of returns were greater than 30%? (Round your answer to 2 decimal places.) Percentage of returns 228% ces b. What percentage of returns were below -2%? (Round your answer to 2 decimal places.) Percentage of returns 93 32% < Prey 6 of 6 Next 0730_14....9 ype here to search O 61% Pre Insert > 2 3 5 6 7 8 O Badge Lock 1 V E R T Y U O G H K Enter 4 C V B N M Shift Alt Poup Ctri → Home Poon End

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Answer 1

A) What percentage of returns were greater than 30%

The percentage returs were greater than A)pl«> 30%) Bor is We know that .2=X- 2= 16 30-14 8 8 ZEZ : pl2>30%) = P(272) = 0.0228 = 2.28% : PC2>30%) = 2.28% (from Z distribution Table

Here P(z>2) = 0.0228 is taken from Z-distribution Table

B) What percentage of returns were Below -2%

6) P(X -2) kle know that ZE X-u Z = -2-14 8 -16 8 17 -2 2--2 ::P(22-27) = P122-2) = 0.0228 : Pl22-2) = 2.28% (from Table) z distribution

P(z<-2) = 0.0228 is taken from Z-distribution Table

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