Question

Human blood pressure levels are normally distributed. If you measured an individual's blood pressure and found the blood pressure level to have a z-score of 2.1, what would you conclude about that person?

Answer 1

Answer:

This value means that the score for this specific person is 2.1 deviations above the true mean $\mu$. And we can find the percentile for this person like this:

$P(Z<2.1) =0.982$

So this person is approximately on the 98 percentile of the distribution.

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

$X \sim N(\mu,\sigma)$  

The z score is given by this formula:

$z=\frac{x-\mu}{\sigma}[/tex ]

And for this case we got z =2.1

This value means that the score for this specific person is 2.1 deviations above the true mean . And we can find the percentile for this person like this:

[tex]P(Z<2.1) =0.982$

So this person is approximately on the 98 percentile of the distribution.