Assume that blood pressure readings are normally distributed with μ = 122 and σ = 7.5. A researcher wishes to select people for a study but wants to exclude the top and bottom 10 percent. What would be the upper and lower readings to qualify people to participate in the study?

And if we solve for a we got

So the value of height that separates the bottom 10% of data from the top 90% is 112.4.  

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

Where and

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

For this part we want to find a value a, such that we satisfy this condition:

  (a)

  (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 01 of the area on the left and 0.90 of the area on the right it's z=-11.28. On this case P(Z<-1.28)=0.10 and P(z>-1.28)=0.9

If we use condition (b) from previous we have this:

If we use condition (b) from previous we have this:

But we know which value of z satisfy the previous equation so then we can do this:

And if we solve for a we got

So the value of height that separates the bottom 10% of data from the top 90% is 112.4.  

x=half

step-by-step explanation:

sine

step-by-step explanation: