Mathematics: 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

Actually, it is a repeating decimal with an 18-digit repeat....

IQ scores are normally normally distributed with

Ответ:

khamyah96

21.01.2022

Mathematics

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:

$\mu = 100, \sigma = 15$