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 5.7 percent and a standard deviation of 9.4 percent.

What is the probability that your return on these bonds will be less than 3.7 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

excel function

NORMDIST(x,mean,standard deviation,cumulative)

mean = 5.7%

standard deviation = 9.4%

a)

P(X<-3.7)

= NORMDIST(-3.7 , 5.7,9.4,TRUE)

= 0.1587

b)

In normal distribution , 68% percent of data is within 1 standard deviation

hence

lower bound = 5.7 - 9.4 = -3.7

upper bound = 5.7 + 9.4 = 15.1

c)

in normal distribution , 95% percent of data is within 2 standard deviation

lower bound = 5.7 - 2 * 9.4 = -13.1

upper bound = 5.7 + 2 * 9.4 = 24.5

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