Question

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.

shaded region is 0.2969

Answer 1

Using the normal distribution, the indicated IQ score is of 108.025.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

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

• The z-score measures how many standard deviations the measure is above or below the mean.

• Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

$\mu = 100, \sigma = 15$.

The shared region is the region to the right, hence it has a p-value of 1 - 0.2969 = 0.7031, which means that Z = 0.535. Then the IQ score is found as follows:

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

0.535 = (X - 100)/15

X - 100 = 0.535 x 15

X = 108.025.

More can be learned about the normal distribution at https://brainly.com/question/15181104

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