A consensus forecast is the average of a large number of individual analysts\' f

Question

A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose the individual forecasts for a particular interest rate are normally distributed with a mean of 5 percent and a standard deviation of 2.0 percent. A single analyst is randomly selected. Find the probability that his/her forecast is

A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose the individual forecasts for a particular interest rate are normally distributed with a mean of 5 percent and a standard deviation of 2.0 percent. A single analyst is randomly selected. Find the probability that his/her forecast is

Explanation / Answer

mean 5%

sd 2%

a)

P(X>=3.7%)

1-P(X<3.7%)

1-P(Z<(3.7%-5%)/2%)

1-P(Z<-0.65)

=1-NORMSDIST(-0.65)

0.7422

b)

P(X<=8%)

P(Z<(8%-5%)/2%)

P(Z<1.5)

=NORMSDIST(1.5)

0.9332

c)

P(3.7%<X<8%)

P(X<8%)-P(X<3.7%)

P(Z<(8%-5%)/2%)-P(X<(3.7%-5%)/2%)

P(Z<1.5)-P(Z<-.65)

=NORMSDIST(1.5)-NORMSDIST(-0.65)

0.6753

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