Use the following information for the next two problems. Harris Company is evaluating the introduction of a new product. The possible levels of unit sales and the probabilities are: Possible Market Reaction Sales in Units Probabilities Low response...................... 40 .20 Moderate response............... 60 .30 High response...................... 80 .50 What is the expected value of unit sales for the new product? What is the standard deviation of unit sales?
The expected value of unit sales for the new product
Expected value of unit = Sum(Number of units x Probability)
= (40 Units x 0.20) + (60 Units x 0.30) + (80 Units x 0.50)
= 8 Units + 18 Units + 40 Units
= 66 Units
Standard deviation of unit sales
Firstly, Calculate the Variance of the units
Variance = [(40 - 66)2 x 0.20] + [(60 - 66)2 x 0.30] +[(80 - 66)2 x 0.50]
= [676 x 0.20] + [36 x 0.30] + 196 x 0.50]
= 135.20 + 10.80 + 98
= 244 Units
Standard Deviation = (244)1/2 or the Square Roof of 244
= 15.62 Units
“Therefore, the Standard deviation of unit sales would be 15.62 Units”
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