Question

Two different designs on a new line of winter jackets for the coming winter are available for your manufacturing plants. Your profit (in thousands of dollars) will depend on the taste of the consumers when winter arrives. The probability of the three possible different tastes of the consumers and the corresponding profits are presented in the following table.

Hint Discrete Probability

Probability	Taste	Design A	Design B
0.2	more conservative	180	520
0.5	no change	230	310
0.3	more liberal	350	270

1. 6)
   

Referring to Table 5-8, what is the variance of your profit when Design A is chosen?

2 Referring to Table 5-8, which design has the better Standard Deviation and why?

Answer 1

Variance for design A.....is nothing but sum of squres of differences between profit and it's mean value.....

Variance=1/3((180-253.33)²+(230-253.33)²+(350-253.33)²)

^{Variance = 5088.88. And Standard Deviation= 71.33}

^{Variance for design B = 12022 and Standard Deviation=109.6458}

^{Therefore design A has better S..D. due to it has less variability than design B......have higher difference between observed and mean values....}

^{Therefore Design A has better Standard..Deviation. than Design B}