Suppose the returns on longterm government bonds are normall

Suppose the returns on long-term government bonds are normally distributed. Assume long-term government bonds have a mean return of 5.9 percent and a standard deviation of 9.2 percent. Requirement 1: What is the probability that your return on these bonds will be less than 3.3 percent in a given year? Use the NORMDIST function in Excel ® to answer this question. (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (eg., 32.16).) Probability % Requirement 2: What range of returns would you expect to see 68 percent of the time? (Negative amount 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. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).) Expected range of returns % to % Requirement 3: What range would you expect to see 95 percent of the time? (Negative amount 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. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).) Expected range of returns % to %

Solution

the returns on long-term government bonds are normally distributed......
mean= 5.9...and s.d = 9.2......
let , x = return on these bonds

a) p (x < - 3.3 ) = p ( z < (-3.3 - 5.9) / 9.2 ) = p ( z < -1 ) =  0.158655 [ you have type- \" NORMDIST(-1) \" in a cell in EXCEL ] i.e = 15.86 %

b) z-score for 68% =+ or, - 0.9944579......

0.9944579 = [ ( 5.9 - (0.9944579 * 9.2 ) , ( 5.9 + (0.9944579* 9.2 ) ] = [ -3.249013 , 15.04901 ]
i.e, - 3.25% to 15.05%..

c) z-score for 95% confidence interval = + or - 1.959964......

Confidence interval= [ 5.9- (1.959964* 9.2) , 5.9 + (1.959964*9.2) ] = [ -12.13167 , 23.93167 ].......
i.e, -12.13 % to 23.93%.......