1. Two cars with six-cylinder engines and three with four-cylinder engines are t

Question

1. Two cars with six-cylinder engines and three with four-cylinder engines are to be driven over a 300-mile course. Let , , ... , , denote the resulting fuel efficiencies (mpg), and they are

125
independently normally distributed. (Mu)1 = (Mu)2 = 22, (Mu)3 = (Mu)4 = (Mu)5 = 26. (Sigma)1 = (Sigma)2 = 1.2, (Sigma)3 =(Sigma)4 = (Sigma)5 = 1.5. Consider the linear combination

Which is a measure of the difference between four-cylinder and six-cylinder vehicles. Compute

P(0 ? ) and P(Y>-2). [Hint: with

Explanation / Answer

For M~N(a,b) and K~N(c,d) independent normal random variables. b and d are the respective variances

xM+yK ~ N(ax+cy , x2b+y2d)

So, Y~ N(22-26, 2*1.22/4+3*1.52/9)=N( -4, 1.22/2+3*1.52/3)=N(-4 ,1.47)

P(Y<=0)=0.997

P(Y>-2)=1-P(Y<=-2)=1-0.913=0.087

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