An investment portfolio contains stocks of a large number of corporations. Over the last year the rates of return on these corporate stocks followed a normal distribution with mean 12.2% and standard deviation 7.2%.
a. For what proportion of these corporations was the rate of return higher than 20%?
b. For what proportion of these corporations was the rate of return negative?
c. For what proportion of these corporations was the rate of return between 5% and 15%?
Answers
Given : An investment portfolio contains stocks of a large number of corporations. Over the last year the rates of return on these corporate stocks followed a normal distribution with mean 12.2% and standard deviation 7.2%.
To Find : a. For what proportion of these corporations was the rate of return higher than 20%?
b. For what proportion of these corporations was the rate of return negative?
c. For what proportion of these corporations was the rate of return between 5% and 15%?
Solution:
Mean = 12.2
SD ( standard deviation) = 7.2
Z score = ( Value - Mean )/SD
rate of return higher than 20%
Z score = ( 20 - 12.2 )/7.2
= 1.08
86 % Data is below this z score
Hence 14 % ( 0.14) proportion of these corporations was the rate of return higher than 20%
rate of return negative => Value = 0
Z score = (0 - 12.2 )/7.2
= - 1.694
4.5 % Data is below this z score
Hence 4.5 % or 0.045 proportion of these corporations was the rate of return negative
rate of return between 5% and 15%
Z score for 5 % = (5 - 12.2 )/7.2 = - 1 => 15.9 % Less than this
Z score for 15 % = (15 - 12.2 )/7.2 = 0.389 => 65.1 Less than this
In between = 65.1 - 15.9
= 49.2 % or 0.492 proportion of these corporations was the rate of return between 5% and 15%
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