Question

IQ scores are normally normally distributed with a mean of 100 and center deviation of 15 if one person is randomly selected what is the probability that the persons IQ far between 110 and 130

Answer 1

Answer:

22.86% probability that the persons IQ is between 110 and 130

Step-by-step explanation:

Problems of normally distributed samples are 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 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:

$\mu = 100, \sigma = 15$

If one person is randomly selected what is the probability that the persons IQ is between 110 and 130

This is the pvalue of Z when X = 130 subtracted by the pvalue of Z when X = 110.

X = 130

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

$Z = \frac{130 - 100}{15}$

$Z = 2$

$Z = 2$ has a pvalue of 0.9772

X = 110

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

$Z = \frac{110 - 100}{15}$

$Z = 0.67$

$Z = 0.67$ has a pvalue of 0.7486

0.9772 - 0.7486 = 0.2286

22.86% probability that the persons IQ is between 110 and 130