Problem 52 Medium Difficulty

Football The margin of victory over the point spread (defined as the number of points scored by the favored team minus the number of points scored by the underdog minus the point spread, which is the difference between the previous two, a spread, which is the difference between the previous two, as
predicted by oddsmakers) in National Football League games has been found to be normally distributed with mean 0 and standard deviation $13.861 .$ Suppose New England is favored over Miami by 3 points. What is the probability that New England wins? (Hint: Calculate the probability that the margin of victory
over the point spread is greater than $-3 .$ ) Source: The American Statistician.

Answer

0.5871

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Calculus 1 / AB

Finite Mathematics and Calculus with Applications

Chapter 18

Probability and Calculus

Section 3

Special Probability Density Functions

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Video Transcript

Okay, So for this question, we're told that we have normally distributed random variable with me and zero standard deviation 13.861 And we won't know the probability that X is greater than negative three. So this is equal to one, minus the probability that X is less than negative three. And so, if we standardize are very well here, this is the probability that a standard normalcy is less than or equal to make a three minus 13 point 861 She is negative. Three minus zero, divided by 13.861 s O negative three divided by 13.61 gives us point negative point to 164 So we're gonna solve this by looking up our value on RZ table. We'll need the negative side of it because we've got a negative number here. It's let's side of the way a little bit and we're looking for negative 2.2. If we round Negative too. 0.2, this here. So one man s point for 1 to 9, and this would give us 0.5 eight 71 as the final answer

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