a. Expected profit
Business Y
Boom 0.2 x 900 = 180
Normal 0.5 x 800 = 400
Recession 0.3 x 700 = 210
Total expected Profit for Y = 790
Business Z
Boom 0.2 x 1000 = 200
Normal 0.5 x 800 = 400
Recession 0.3 x 600 = 180
Total expected Profit for Z = 780
b.
I will select business Y because it has a higher expected profit as compared to business Z.
c.
Discrete Probability distribution of Y
y p(y)
180 0.2
400 0.5
210 0.3
Discrete Probability distribution of Z
z p(z)
200 0.2
400 0.5
180 0.3
I will select business Z
d.
Expected Mean
Expected mean for business Y
y p(y) y*p(y)
180 0.2 36
400 0.5 200
210 0.3 63
Expected mean for Y = 299
Expected mean for Z
z p(z) z*p(z)
200 0.2 40
400 0.5 200
180 0.3 54
Expected mean for Z = 294
Based on the expected mean I will choose business Y
Variance
Variance for Business Y
(y – μ)2 * P(y)
(180-299)2 * 0.2 =2832.2
(400-299)2 * 0.5 =5100.5
(210-299)2 * 0.3 =2376.3
Total variance for Y = 10309
Standard deviation
Standard deviation of Y is the square root of the variance = 101.53
Variance
Variance for Business Z
(z – μ)2 * P(z)
(200-294)2 * 0.2 =1767.2
(400-294)2 * 0.5 =5618
(180-294)2 * 0.3 =3898.8
Total variance for Z = 11284
Standard deviation
Standard deviation of Z is the square root of the variance = 106.23
Coefficient of variation
Coefficient of variation is given by the standard deviation divided by the mean
Coefficient of variation of Y is 101.53 / 299 = 0.34
Coefficient of variation of Z is 106.23 / 294 = 0.36
Based on the variance, standard deviation and coefficient of variation I will choose business Y.
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