Answer:
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:
