Question

Suppose the returns on long-term government bonds are normally distributed. Assume long-term government bonds have a mean return of 5.3 percent and a standard deviation of 8.8 percent.

What is the probability that your return on these bonds will be less than −3.5 percent in a given year? Use the NORMDIST function in Excel® to answer this question. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Probability             %

What range of returns would you expect to see 68 percent of the time? (A negative answer should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected range of returns             % to %

What range would you expect to see 95 percent of the time? (A negative answer should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected range of returns             % to %

Answer 1

В 14 a) Probability of return less than -3.5% 15 15.87% =NORMDIST(-3.5%,5.3%,8.8%, TRUE) 17 b) At 68%: 18 Expected range of returns Mean-Standard deviations to Mean+Standard deviations Expected range of returns to -3.50% =5.3%-8.8% 14.10% =5.3%+8.8% 22 c) At 95: Expected range of returns Mean-[2xStandard deviations] to Expected range of returns -12.30% to Mean+(2xStandard deviations] 22.90% =5.3%+2*8.8% =5.3%-2*8.8%

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