Question

See below. I have the excel formula for a-c, i need to know how to calculate d-f in excel.

The Wall Street Journal reported that long term Treasury bonds had a mean return of 24.03% in 2008. Assume that the returns for the long term Treasury bonds were distributed as a normal random variable, with a mean of 24.03 and a standard deviation of 10. If you select an individual Treasury bond from this population, what is the probability that it would have a return of...

a.      less than 0 (a loss)?

=NORMDIST(0,24.03,10,TRUE) .0081

b.     between 10 and 20 ?

=NORMDIST(20,24.03,10,TRUE)-NORM.DIST(10,24.03,10,TRUE) .2632

c.    greater than 10 ?

=1-NORMDIST(10,24.03,10,TRUE) .9197

If you select a random sample of 4 Treasure bonds from this population, what is the probability that the sample would have a mean return of...

d. less than 0 (a loss)?

e. between 10 and 20 ?

f. greater than 10 ?

Answer 1

d)

here, std dev of sampling distribution  = σ/√n = 10/√4 = 10/2 = 5

P(X<0 ) = 0.000000770

=NORMDIST(0,24.03,2,TRUE)

e)

=NORMDIST(20,24.03,2,TRUE)-NORM.DIST(10,24.03,2,TRUE)  

answer: 0.2076

f)

=1-NORMDIST(10,24.03,2,TRUE)

answer: 0.9975

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OR you can directly use,

d) =NORMDIST(0,24.03,10/sqrt(4),TRUE)

e) =NORMDIST(20,24.03,10/sqrt(4),TRUE)-NORM.DIST(10,24.03,10/sqrt(4),TRUE)  

f) =1-NORMDIST(10,24.03,10/sqrt(4),TRUE) .9197