Question

If IQ scores are normally distributed with a mean of 100 and a standard deviation of 15, what is the mean IQ score after the scores have been standardized by converting them to z-scores?

Answer 1

Answer:

$\mu = 0 , \sigma=1$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the IQ scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(100,15)$  

Where $\mu=100$ and $\sigma=15$

If we standardize the variable with the z score given by:

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

We got a normal standard distribution with parameters $Z\sim N (0,1)$

$\mu = 0 , \sigma=1$