Question

Suppose that diastolic blood pressure readins of adult male have a bell-shaped distribution with a mean of 84 mmHg and a standard deviation of 9 mmHg. Using the empirical rule, what percentage of adult males have a diastolic blood pressure readings that are greater than 102 mmHg? Please do not round your answer.

Answer 1

Solution:

    We are given that: the diastolic blood pressure readings of the adult male have a bell-shaped distribution with a mean of 84 mmHg and a standard deviation of 9 mmHg.

That is: Mean = and Standard Deviation =

We have to use an Empirical rule to find the percentage of adult males have a diastolic blood pressure readings that are greater than 102 mmHg.

According to an Empirical rule:

for bell-shaped distribution ( Normal distribution )

1) 68% of the data falls within 1 standard deviation from mean
that is :
2) 95% of the data falls within 2 standard deviations from mean
that is :

3) 99.7% of the data falls within 3 standard deviations from mean
that is :

Thus find:

That means 68% of the data is in between 75 and 93.

Now find:

Thus 95% of the data is between 66 and 102.

Then, the remaining 5% data is equally divided in two tails:

That is half of 5% is below 66 and half of 5% is above 102.

Thus 5%/2 = 2.5% is below 66 and 2.5% is above 102.

Thus 2.5% of adult males have a diastolic blood pressure readings that are greater than 102 mmHg.