A distribution has a standard deviation of o=10. Find the z-score for each of the following locations in the distribution.

a. Above the mean by 5 points.

b. Above the mean by 2 points.

c. Below th mean by 20 points.

d. Below the mean by 15 points.

a) Using the z score formula we got:

b) Using the z score formula we got:

c) Using the z score formula we got:

d) Using the z score formula 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 variable os interest of a population, and for this case we know the distribution for X is given by:

Where and

The best way to solve this problem is using the normal standard distribution and the z score given by:

Part a

Using the z score formula we got:

Part b

Using the z score formula we got:

Part c

Using the z score formula we got:

Part d

Using the z score formula we got:

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