Mathematics: 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 distribution has a standard deviation of o=10.

Ответ:

danidavis2002

20.01.2022

Mathematics

a) Using the z score formula we got:

$z = \frac{\mu +5 -\mu}{\sigma}= \frac{5}{10}= 0.5$

b) Using the z score formula we got:

$z = \frac{\mu +2 -\mu}{\sigma}= \frac{2}{10}= 0.2$

c) Using the z score formula we got:

$z = \frac{\mu -20 -\mu}{\sigma}= -\frac{20}{10}= -2$

d) Using the z score formula we got:

$z = \frac{\mu -15 -\mu}{\sigma}= -\frac{15}{10}= -1.5$

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:

$X \sim N(\mu,10)$