The mean systolic blood pressure of adult males is normally

distributed with a mean of 138 (millimeters of
mercury) and a standard deviation of 9.7. What percent
of adult males have blood pressure between 161.28 and
164.9?

check out this webpage

http://davidmlane.com/hyperstat/z_table.html

Just enter the mean and sd
click on 'between' and enter your values.

To find the percentage of adult males who have blood pressure between 161.28 and 164.9, we can use the concept of the standard normal distribution.

Step 1: Standardize the values
First, we need to convert the given values to z-scores using the formula:
z = (x - μ) / σ
where x is the observed value, μ is the mean, and σ is the standard deviation.

For the lower value (161.28):
z1 = (161.28 - 138) / 9.7

For the higher value (164.9):
z2 = (164.9 - 138) / 9.7

Step 2: Calculate the corresponding areas under the standard normal curve
Next, we need to find the area under the standard normal curve between these two z-scores. We can use a standard normal distribution table or a calculator to find these values.

Let's assume the area between z1 and z2 is represented by P(Z1 ≤ Z ≤ Z2).

Step 3: Convert the z-scores back to the original scale
Finally, we need to convert the standardized values back to the original scale using the formula:
x = z * σ + μ

For the lower value:
x1 = z1 * 9.7 + 138

For the higher value:
x2 = z2 * 9.7 + 138

The percentage of adult males with blood pressure between 161.28 and 164.9 is given by:
P(x1 ≤ X ≤ x2) = P(Z1 ≤ Z ≤ Z2)

By following these steps, you can calculate the percentage of adult males with blood pressure in the specified range.