IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. If a certain statistician has an IQ of 122, what percent of the population has an IQ less than she does?

A. 7%
B. 22%
C. 93%
D. 99%
E. 47%

Question

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. If a certain statistician has an IQ of 122, what percent of the population has an IQ less than she does?


 		A.	7%
 		B.	22%
 		C.	93%
 		D.	99%
 		E.	47%

anonymous · Answer

$z=\frac{x-\mu}{\sigma}=\frac{122-100}{15}=1.4667$

Then use a z-table to find the percentage.

directrix · Answer

C. 93%
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Following from above, a Z-score of 1.4667 has area approximately .4279 between the z-score and the mean. To the left of the mean is .5000 area. Added, the area is .9279 which is roughly 93% of the population with IQ less than that of the statistician.

hba · Answer

ur done with it