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Nataly [62]
3 years ago
15

Find the indicated IQ score. The graph depicts IQ scores of adults, and those scores are normally distributed with a mean of 100

and a standard
deviation of 15 (as on the Wechsler test).
The shaded area under the curve is 0.5675.
Mathematics
1 answer:
Taya2010 [7]3 years ago
8 0

Answer:

IQ score of 102.55

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score, measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value, which is also the shaded area under the curve, is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 100, \sigma = 15

The shaded area under the curve is 0.5675.

This means that Z has a pvalue of 0.5675.

So, we have to find X when Z = 0.17.

Z = \frac{X - \mu}{\sigma}

0.17 = \frac{X - 100}{15}

X - 100 = 15*0.17

X = 102.55

IQ score of 102.55

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