SOLUTION: Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

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Question 1167991: Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.
The shaded area is on the right of the curve. It is X=0.1753.
I need the Z score and use the z score to find the indicated IQ score.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the mean is 100 and the standard deviation is 15.

the shaded area on the right of the distribution curve represents an area of .1753 * the area under the normal distribution curve.

the area under the normal distributive curve is equal to 1.

the 1 represents 100% of the area under the normal distribution curve.

the .1753 represents 17.53% of the area under the normal distribution curve.

you are looking for a z-score that has an area of .1753 to the right of it.

subtract that from 1 and you are looking for a z-score that has an area of .8247 to the left of it.

a z-score calculator helps here.

the one that i have on my ti-84 plus calculator tells me that a z-score with an area of .8247 to the left of it is equal to .9334 rounded to 4 decimal places.

graphically, this looks like the following.

the first graph shows the z-score with an area to the left of it of .8247.

the second graph shows the z-score with an area to the right of it of .1753

it's the same z-score of .9334.

this confirms that the area to the right of the z-score is equal to 1 minus the area to the left of it.

this also confirms that the area to the left of the z-score is equal to 1 minus the area to the right of it.

if you have one, you can get the other one by taking 1 minus the area.

now that you know the z-score, you can solve for the raw score.

your mean is 100 and your standard deviation is 15.

the z-score formula is:

z = (x - m) / s

z is the z-score.
x is the raw score.
m is the raw mean.
s can be the standard deviation or the standard error.
in this case, s represents the standard deviation.

when the z-score is .9334, and the mean is 100 and the standard deviation is 15, the z-score formula becomes:

.9334 = (x - 100) / 15

solve for x to get:

x = .9334 * 15 + 100 = 114.001

that's your raw score.

that means that the IQ score that has .1753 * the area under the normal distribution curve to the right of it is equal to 114.001

it also means that the IQ score that has .8247 * the area under the normal distribution curve to the left of it is equal to 114.001.

this can be seen in the following two displays.

the first display shows the area to the right of the indicated IQ.

the second display shows the area to the left of the indicated IQ.

the IQ is the same in both cases, as it should be because the area to the right of the indicated IQ score is equal to 1 minus the area to the left of the indicated IQ score, and vice versa.

your solution is that the IQ score that has an area of .1753 * the area under the normal distribution curve is 114.001.

once again, the complete area under the normal distribution curve is assumed to be 1.

the normal z-score calculator that was used to provide these displays can be found at http://davidmlane.com/hyperstat/z_table.html

SOLUTION: Find the indicated IQ score. The graph to the right depicts IQ scores of​ adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.

SOLUTION: Find the indicated IQ score. The graph to the right depicts IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15.