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?

Z = (score-mean)/SD

Calculate the two z scores. Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion between these two Z scores.

To find the percentage of adult males with blood pressure between 161.28 and 164.9, we can use the Z-score formula, assuming that the distribution is normal.

The Z-score formula is given by:
Z = (X - μ) / σ

Where:
Z is the standard score or Z-score,
X is the value we want to find the percentile for,
μ is the mean of the distribution, and
σ is the standard deviation of the distribution.

First, we need to find the Z-scores for 161.28 and 164.9.

For 161.28:
Z1 = (161.28 - 138) / 9.7

For 164.9:
Z2 = (164.9 - 138) / 9.7

Next, we can use a Z-table or a statistical calculator to find the area or percentage between these two Z-scores. The area represents the proportion or percentage of the distribution that falls between the given values.

Finally, subtract the lower percentage from the higher percentage to find the percentage of adult males with blood pressure between 161.28 and 164.9.