Diastolic blood pressure is a measure of the pressure when arteries rest between heartbeats. suppose diastolic blood pressure levels in women are normally distributed with a mean of 69.3mm hg and a standard deviation of 8.8mm hg. complete parts (a) and (b) below.

a. a diastolic blood pressure level above 90 mm hg is considered to be hypertension. what percentage of women have hypertension?

b. if we randomly collect samples of women with 16 in each sample, what percentage of those samples have a mean above 90 mm hg?

a)

b)

And using a calculator, excel ir the normal standard table we have that:

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".  The letter is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words:

Let X the random variable that represent the blood pressure for women, and for this case we know the distribution for X is given by:

Where and

Part a

We are interested on this probability

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

If we apply this formula to our probability we got this:

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

Part b

The distribution for the sample mean on this case is given by:

And we want to calculate the following probability:

And using a calculator, excel ir the normal standard table we have that:

i found two solutions,   n = 2 • ± √3 = ± 3.4641

step-by-step explanation: