Question

IQ scores are normally distributed with a mean of 100 and a standard deviation of 15.

Answer 1

Using the normal distribution, it is found that 1851 people would have an IQ less than 115.

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 proportion of IQ scores less than 115 is the p-value of Z when X = 115, hence:

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

$Z = \frac{115 - 100}{15}$

Z = 1

Z = 1 has a p-value of 0.8413.

Out of 2200 people:

0.8413 x 2200 = 1851.

More can be learned about the normal distribution at brainly.com/question/27643290

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