Sales Distribution 1 Probability Distribution 2 Probability 2,000 0.05 0.05 3,00
ID: 1199001 • Letter: S
Question
Sales
Distribution 1
Probability
Distribution 2
Probability
2,000
0.05
0.05
3,000
0.20
0.15
4,000
0.50
0.20
5,000
0.20
0.35
6,000
0.05
0.25
a. For Distribution 1, the expected sales are ________ . For Distribution 2, the expected sales are _______
b. For Distribution 1, the variance is _______ For Distribution 2, the variance is _________
c. For Distribution 1, the standard deviation is ______________. For Distribution 2, the standard deviation is ______________.
d. Distribution ____ is the riskier of the two distributions of sales.
e. For Distribution 1, the coefficient of variation is ______________. For Distribution 2, the coefficient of variation is ______________. Distribution _____ has the greater level of risk relative to its mean.
Sales
Distribution 1
Probability
Distribution 2
Probability
2,000
0.05
0.05
3,000
0.20
0.15
4,000
0.50
0.20
5,000
0.20
0.35
6,000
0.05
0.25
Explanation / Answer
a) Distribution 1: Expected sales = sales* distribution 1 probability
= 4000
Distribution 2: Expected sales = sales* distribution 2 probability
= 4600
b) Variance for distribution 1 = E(X2P) - (E(XP))2 = 800000
Variance for distribution 2 = E(X2P) - (E(XP))2 = 1340000
C) Standard deviation = squareroot(variance)
Distribution1 = 894.4
Distribution 2 = 1157.5
d) Distribution 2 is riskier as it has higher standard deviation
e) Coefficient of variation = standard deviation/mean
Distribution 1: coefficient of variation = 22%
Distribution 2: Coefficient of variation = 25%
Distribution 2 has greater level of risk relative to its mean.
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