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 5.2 percent and a standard deviation of 8.7 percent. Requirement 1: What is the approximate probability that your return on these bonds will be less than 3.5 percent in a given year? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).)   Probability % Requirement 2: What range of returns would you expect to see 95 percent of the time? (Do not include the percent signs (%). Negative amount should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Round your answers to 2 decimal places (e.g., 32.16).)   Expected range of returns % to % Requirement 3: What range would you expect to see 99 percent of the time? (Do not include the percent signs (%). Negative amount should be indicated by a minus sign. Input your answers from lowest to highest to receive credit for your answers. Round your answers to 2 decimal places (e.g., 32.16).)   Expected range of returns % to % I only need to probability %.

Explanation / Answer

mean=5.2% std=8.7%
as per normal distribution Z=(x-mean)/std
Here X=3.5%
Z=(-3.5%-5.2%)/8.7%
=-1
P(Z<-1)=15.87%
b) 95% of time the Z value is between +-2
X=(mean+2*std) to (mean-2*std)
=(5.2%+(2*8.7%) to (5.2%-(2*8.7%))
=-12.22% to 22.60%

c)for 99% of time it is between +- 3 std
X=(mean+3*std) to (mean-3*std)
=(5.2%+(3*8.7%) to (5.2%-(3*8.7%))
=-20.90% to 31.30%

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