A consensus forecast is the average of a large number of individual analysts’ fo

Question

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 3 percent and a standard deviation of 1.7 percent. (Round k, Q1, 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.

Find the first quartile, Q1, and the third quartile, Q3, of the distribution of individual forecasts. Follow the methods outlined in part a, or compute the inverse cdf in MINITAB.

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.

Explanation / Answer

a) here for 10 percentile lies atr z=-1.28155

10th percentile of the distribution of individual forecasts =mean +z*std deviation =0.8214%

b)25 th percentile lies at z=-0.6745

Q1 =1.8534

similarly 75 th percentile. z=0.6745

Q3=4.1466

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