Respuesta :
Answer:
[tex]\mu = 0 , \sigma=1[/tex]
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:
[tex]X \sim N(100,15)[/tex]
Where [tex]\mu=100[/tex] and [tex]\sigma=15[/tex]
If we standardize the variable with the z score given by:
[tex] Z= \frac{x -\mu}{\sigma}[/tex]
We got a normal standard distribution with parameters [tex] Z\sim N (0,1)[/tex]
[tex]\mu = 0 , \sigma=1[/tex]
