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 6 percent and a standard deviation of 1.4 percent. A single analyst is randomly selected. Find the probability that his/her forecast is

(a) At least 3.3 percent. (Round your answer to 4 decimal places.)

P            

(b) At most 7 percent. (Round your answer to 4 decimal places.)

P            

(c) Between 3.3 percent and 7 percent. (Round your answer to 4 decimal places.)

P            

Explanation / Answer

Mean is 6 and s is 1.4. z can be calculated as (x-mean)/s

a) P(x>3.3) =P(z>(3.3-6)/1.4)=P(z>-1.93)=P(z<1.93). From the normal distribution table we get 0.9732

b) P(x<7)=P(z<(7-6)/1.4)=P(z<0.71). from normal table it is 0.7611

c) P(3.3<x<7)=P(x<7)-P(x<3.3)=0.7611-(1-0.9732)=0.7343

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