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?

Try this wonderful program,

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

You can convert to data to z-scores or use it directly

It is preset for a mean of 0 and SD of 1

To find the percentage of adult males with blood pressure between 161.28 and 164.9, we need to calculate the area under the normal distribution curve between these two values.

We can use the z-score formula to convert the given blood pressure values into z-scores. A z-score represents the number of standard deviations an individual value is from the mean.

The formula for calculating the z-score is:

z = (x - μ) / σ

Where:
x = the individual blood pressure value
μ = the mean of the distribution
σ = the standard deviation of the distribution

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

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

Next, we can use a standard normal table or a calculator to find the corresponding probabilities for these z-scores. The area between these two z-scores will give us the percentage of adult males with blood pressure within this range.

Using a standard normal table or calculator, we find:

The probability corresponding to z1 is P(Z ≤ z1).
The probability corresponding to z2 is P(Z ≤ z2).

To find the probability between these two values, we subtract the lower probability from the higher probability:

P(Z ≤ z2) - P(Z ≤ z1)

Finally, we multiply this probability by 100 to convert it to a percentage:

(P(Z ≤ z2) - P(Z ≤ z1)) * 100

Calculating these values, we can find the percentage of adult males with blood pressure between 161.28 and 164.9.