For males in a certain town, the systolic blood pressure is normally distributed with a mean of 125 and a standard deviation of Using the empirical rule, what percentage of males in the town have a systolic blood pressure between 120 and 130?
To find the percentage of males with a systolic blood pressure between 120 and 130, we first need to calculate the z-scores for each of these values.
For a systolic blood pressure of 120:
z = (120 - 125) / 10 = -0.5
For a systolic blood pressure of 130:
z = (130 - 125) / 10 = 0.5
Now, we need to find the area under the normal curve between these two z-score values. Using the empirical rule, we know that about 68% of the data falls within one standard deviation of the mean, so we can calculate this by finding the area between z = -0.5 and z = 0.5.
Using a standard normal distribution table or a calculator, we can find that the area between z = -0.5 and z = 0.5 is approximately 0.3829.
Therefore, approximately 38.29% of males in the town have a systolic blood pressure between 120 and 130.