Which team scores higher?

Question

Team A's score is normally distributed with mean 75 and standard deviation 6. Team B's score is normally distributed with mean 70 and standard deviation 8. The two scores are independent.

What is the probability that Team A scores higher than Team B?

Accepted Answer

Compare the two scores through their difference. Let D = (	ext{A's score}) - (	ext{B's score}). "A scores higher" means D 0. The difference of two independent normals is normal: the mean subtracts, the variances add. Mean of D: \;75 - 70 = 5. Variance of D: \;6^2 + 8^2 = 36 + 64 = 100, so the standard deviation of D is \sqrt{100} = 10. So D is normal with mean 5 and standard deviation 10. Convert 0 to a z-score: z = \frac{0 - 5}{10} = -0.5. We want the area to the right of z = -0.5, about 0.6915: P(D 0) \approx 0.6915. Team A's 5-point average edge is only half a standard deviation of the d…

Which team scores higher?

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