Supplementary Exercise 6.64 A consensus forecast is the average of a large numbe

Question

Supplementary Exercise 6.64 A consensus forecast is the average of a large number of individual analysts' forecasts. Suppose that individual forecasts of a particular interest rate are normally distributed with a mean of 6 percent and a standard deviation of 1.9 percent (Round k, 01. and Q3 to 3 decimal places, and round percentages in part a to the nearest whole number. Round the z value to 3 decimal places in part a and 2 decimals in part b.) What percentage of individual forecasts are at or below the 10th percentile of the distribution of forecasts? What percentage are at or above the 10th percentile? Find the 10th percentile of the distribution of individual forecasts. At or below 10 percentile At or above the 10 percentile Find the first quartile. Q^1. and the third quartile. Q^3, of the distribution of individual forecasts. Follow the methods outlined in part a, or compute the inverse cdf in MINITAB.

Explanation / Answer

a)

By definition,

At or below 10 percentile = 10% [ANSWER]
At or above 10 percentile = 90% [ANSWER]

FOr k:

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.1      
          
Then, using table or technology,          
          
z =    -1.282      
          
As x = u + z * s,          
          
where          
          
u = mean =    6      
z = the critical z score =    -1.282      
s = standard deviation =    1.9      
          
Then          
          
k = critical value =    3.5642   [ANSWER]

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b)

FOR Q1:

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.25      
          
Then, using table or technology,          
          
z =    -0.67      
          
As x = u + z * s,          
          
where          
          
u = mean =    6      
z = the critical z score =    -0.67      
s = standard deviation =    1.9      
          
Then          
          
Q1 = x = critical value =    4.727   [ANSWER]

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FOR Q3:

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.25      
          
Then, using table or technology,          
          
z =    0.67      
          
As x = u + z * s,          
          
where          
          
u = mean =    6      
z = the critical z score =    0.67      
s = standard deviation =    1.9      
          
Then          
          
Q3 = x = critical value =    7.273   [ANSWER]  

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