Joses ACT score had a z-score of .75.what was his ACT score?

mean score=21.1 sd=5.2

Where and

And the z score is given by:

And since z = 0.75 we can replace like this:

And if we solve for x we got:

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:

Where and

And the z score is given by:

And since z = 0.75 we can replace like this:

And if we solve for x we got:

the 2 figures are congruent bc if you reflect abcd over the y axis then over the d axis the figures overlap

substitute,

circle 1 = 5

circle 2 = 20

circle 3 = 44

in this case no matter how you add, you will always get a perfect square..

hence proved

happy to

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