Question

Joses ACT score had a z-score of .75.what was his ACT score? mean score=21.1 sd=5.2

Answer 1

Answer:

$X \sim N(21.1,5.2)$  

Where $\mu=21.1$ and $\sigma=5.2$

And the z score is given by:

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

And since z = 0.75 we can replace like this:

$0.75 = \frac{x- 21.1}{5.2}$

And if we solve for x we got:

$x = 21.1 +0.75*5.2 = 25$

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 ACT scores of a population, and for this case we know the distribution for X is given by:

$X \sim N(21.1,5.2)$  

Where $\mu=21.1$ and $\sigma=5.2$

And the z score is given by:

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

And since z = 0.75 we can replace like this:

$0.75 = \frac{x- 21.1}{5.2}$

And if we solve for x we got:

$x = 21.1 +0.75*5.2 = 25$