SOLUTION: Assume that a set of test scores is normally distributed with a mean of 120 and a standard deviation of 20 . Use the​ 68-95-99.7 rule to find the following quantities.

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Question 1155451: Assume that a set of test scores is normally distributed with a mean of 120

and a standard deviation of 20
.
Use the​ 68-95-99.7 rule to find the following quantities.
A. The percentage of scores less than 120

is _ ?
B. The percentage of scores greater than 140

is _ ?
C. The percentage of scores between 80

and 140

is _ ?
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
The first is the percentage less than the mean. This is half or 50%
The second is (140-120)/20=1 z=(x-mean)/sd
68% are greater than 1 from the mean OR -1 from the mean. Therefore it is 16% that are greater than 1; the other 16% are less than -1 sd s from the mean.
Between 80 and 140, using the same formula, would be between -2 and +1.
Draw the normal curve. Label 3 sd s on either side. From -2 to 0 is 47.5%. From 0 to 1 is 34%. That sum is 81.5%.