SOLUTION: The distribution of scores on a recent quiz in Mr. Waldron's statistics class is approximately normal. About 2.5% of the students scored below 25 on the quiz. 84% of the students s
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Question 1175807: The distribution of scores on a recent quiz in Mr. Waldron's statistics class is approximately normal. About 2.5% of the students scored below 25 on the quiz. 84% of the students scored below 40 on the quiz. Use the 68-95-99.7 rule to estimate the mean and standard deviation of the quiz scores in this class. Make sure to show your work and justify your answer. Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! 2.5% is z=-2 SD by the empiric rule
84% is z=+1 sd by the empiric rule
z=(x-mean)/sd
so
-2=(25-mean)/sd
-2sd=25-mean
mean-2sd=25
-
and
+1=(40-mean)/sd
mean+1=40
-
two equations in two unknowns.
subtract
-3sd=-15
sd=5
mean=35
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mean is 35 and sd is 1
68% are between 30 and 40
16% are above 40 or 84% are below 40
95% are between 25 and 45 so 97.5% are greater than 25 and 2.5% below.
