Suppose the returns on long-term government bonds are normally distributed. Assu

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 %

Explanation / Answer

=normdist(x,mean,std,true)
a)p(z<3.5%)
=normdist(3.5%,5.3%,8.8%,1)
=41.9%
2)68% means 1 sigma so the returns are
=(means+sigma) and (mean-sigma)
=(5.3%+8.8%) and (5.3%-8.8%)
=14.1% and -3.5%
3)95% fo time means 2 sigma from the mean
=(means+2sigma) and (mean-2sigma)
=(5.3%+(2*8.8%)) and (5.3%-(2*8.8%))
=22.9% and -12.3%

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