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Suppose it is known that QB Ratings in the NFL are normally distributed with mean 87.2 and standard deviation 8. Suppose it is known that Russell Wilson, a second year quarterback for the Seattle Seahawks,is ranked in the 87th percentile among all quarterbacks. What was Russell Wilson's QB Ratings?

Ok so I've drawn a bell curve with $\mu$=87.2 and have drawn out +/-1 and +/-2 standard deviations. However I am a bit confused on how to find his quarterback rating.

Can someone give me a hint?

Thanks

EhBabay
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1 Answers1

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Look up 87 percent in your standard normal table. You may have to interpolate between some of the values. The table tells you how many standard deviations above the mean is the 87th percentile. As you are given the standard deviation is 8...

Ross Millikan
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  • Well I will be honest, we haven't even gone over how to read the table. On a vertical axis I have numbers ranging from 0.0 to 3.4 and along the horizontal axis is z ranging from .00 to .09. .8708 is at the point z=.03 and 1.1. Also what are the numbers along the vertical axis. – EhBabay Jan 28 '14 at 21:13
  • The vertical axis is numbers of standard deviations in tenths. The horizontal axis gives the hundredths values. The values in the table are the probability that the value is below mean plus n sigma, where n is the sum of the left column and the top row. You should be able to see that the entries in the table are monotonic. So 1.13 sigma high is above $87.08%$ of the distribution. – Ross Millikan Jan 28 '14 at 21:30