Answer:
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: