Question

QUESTION 4 Five automobiles of the same type are to be driven on a 300-mile trip. The first two will use an economy brand of gasoline, and the other three will use a name brand. Let X. X, X3, X, and X3 be the observed fuel efficiencies (mpg) for the five cars. Suppose these variables are independently distributed with = - 2013 - 14 s = 24, and o7 o 4 for the economy brand and oz-o-o-3.5 for the name brand. Define the ru Y by X1 X2 X3 + X2 + X Y 2 so that Y is a measure of the difference in efficiency between economy gas and name-brand gas. Compute oy.[3 decimal places]

Answer 1

Question 4. $\sigma_{Y}=1.780$

Question 9: The probability is

d. 0.309

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$V(Y)=\frac{1}{2^{2}}\left [ V(X_{1})+V(X_{1}) \right ]+\frac{1}{3^{2}}\left [ V(X_{3})+V(X_{4})+ V(X_{5})\right ]$

$V(Y)=\frac{1}{4}\left [ 4+4 \right ]+\frac{1}{9}\left [ 3.5+3.5+3.5\right ]$

$V(Y)=2+\frac{3*3.5}{9}$

$V(Y)=3.1667$

$\sigma_{Y}=\sqrt{V(Y)}=1.7795$

Question 9: Gestation if X>140. ie $Z=\frac{X-\mu}{\sigma}=\frac{140-135}{10}=\frac{5}{10}=0.5$

ie P(Z>0.5)=1-P(Z<0.5)=1-0.691=0.309