SOLUTION: The scores on a psychology exam were normally distributed with a mean of 52 and a standard deviation of 9. About what percentage of scores were less than 43​? Use the​ 68-95-99

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Question 1206898: The scores on a psychology exam were normally distributed with a mean of 52 and a standard deviation of 9. About what percentage of scores were less than 43​? Use the​ 68-95-99.7 rule.
Found 3 solutions by Theo, ikleyn, greenestamps:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the 68-95-99.7 rule states that:

68% of the z-scores are within 1 standard deviation from the mean.
95% of the z-=scores are within 2 standard deviations from the mean.
99.7% of the z-scores are within 3 standard deviations from the mean.

the empirical rule chart is broken down as shown below.



within 1 standard deviation from the mean is 2 * 34 = 68%.

within 2 standard deviations from the mean is 2 * (34 + 13.5) = 95%.

within 3 standard deviations from the mean is 2 * (34 + 13.5 + 2.35) = 99.7%.

the raw score is 43 and the mean is 52 and the standard deviation is 9.

z-score formula is:

z = (x - m) / s

z is the z-score
x is the raw score
m is the mean
s is the standard deviation.

your z-score is (43 - 52) / 9 = -9/9 = -1.

the area to the left of that z-score is .15% + 2.35% + 13.5% = 16%.

that's a ratio of .16.

if you use a z-score calculator, you would get what is shown below.



that rounds to .1587 which is pretty close to .16.

that's less than 1% off of the actual.
Answer by ikleyn(52799)   (Show Source): You can put this solution on YOUR website!
.
The scores on a psychology exam were normally distributed with a mean of 52
and a standard deviation of 9. About what percentage of scores were less than 43​?
Use the​ 68-95-99.7 rule.
~~~~~~~~~~~~~~~~~~ 

Notice that in this problem the score of 43 is one standard deviation from the mean of 52.


So, using the empirical rule, the percentage of scores that are less than 43 is

     =  = 0.16,  or  16%.    ANSWER

Solved.



Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


Solving in a much less formal manner than in the other responses....

The 68-95-99.7 rule says that 68% of scores are within 1 standard deviation of the mean.
43 is 1 standard deviation below the mean of 52, so half of 68% = 34% of scores are between 43 and the mean.
That means 50%-34% = 16% of scores are below 43.

ANSWER: 16%
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