Both an introductory statistics course for business students and an introductory

Question

Both an introductory statistics course for business students and an introductory biostatistics course use textbooks from the same publisher. The number of business statistics textbook purchased, X, depends on enrollment and the price is $200 per textbook. The number of biostatistics textbooks purchased, Y , also depends on enrollment and the price is $175 per textbook. Since these are both introductory statistics courses, the correlation between X and Y is -0.57. The mean and standard deviation of enrollment in the business statistics class are µX = 531 and X = 11, while the mean and standard deviation of enrollment in the biostatistics class are µY = 238 and Y = 7. Consider the difference in revenue from the business statistics textbooks and the biostatistics textbooks. What is the standard deviation of this difference? (a) $516.79 (b) $1807.85 (c) $2532.13 (d) $3068.05

Explanation / Answer

as here differnce A =200X-175Y

thefore variance of difference =Var(A)=2002Var(X)+1752*Var(Y)-2*200*175*r*(SD(X)*D(Y)

=(200*11)2+(175*7)2-2*200*175*(-0.57)*11*7=9412925

hence std deviation of differnce =(9412925)1/2 =3068.05

option D is correct

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