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Question 1161078: PLEASE HELP ME! I REALLY APPRECIATE ANY SUPPORT!
1) Suppose that the distribution for the number of points scored in a game by Steph Curry can be described by an approximate normal curve, with a mean of 30 and a standard deviation of 8. About how many points are needed to ensure there is only approximately a 2.5% chance that Steph exceeds this amount?
2) Lastly, assume the scoring distribution of Knicks phenom RJ Barret is
approximately normal in shape. Suppose there is approximately 0.15% chance that R.J scores more than 26 points, and a 2.5% chance that he scores less than 6 points. What is his mean and standard deviation of points scored?
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! the 97.5th percentile is 45.68 or 46 points
calculator 2 VARS 3 invnorm (.975,30,8)
99.85 percentile is 2.967 sd
97.5 percentile is 1.96 sd
z=(x-mean)/sd
so 2.967=(x-mean)/sd
and -1.96=(x-mean)/sd
2.97 sd=26-mean
-1.96 sd=6-mean
1.96 sd=-6+mean
4.93 sd=20
sd=4.056 or 4.06 points
(26-mean)=4.06*2.967=12.05
mean=13.95 points
check
26-13.95 divided by 4.06=12.05/4.06 or 2.97 points standard deviation.
and
-7.95/4.06=-1.96 sd
can check using normalcdf (6,26,13.95,4.06), which should be everything but 0.15% on the left and 2.5% on the right or 100-2.65=97.35%, and it is 97.34%
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