Final answer:
Calculate the z-score for blood pressure value of 137 with the given mean and standard deviation. Find the corresponding probability from the standard normal distribution and subtract it from 1. The result is approximately 37.1%, which is the percentage of males with a systolic blood pressure higher than 137 to the nearest tenth.
Step-by-step explanation:
To find the percentage of males in the town with a systolic blood pressure higher than 137 mm Hg, we must first calculate the z-score for the blood pressure value of 137 given the mean (µ) of 135 and the standard deviation (σ) of 6. The z-score is calculated using the formula:
Z = (X - µ) / σ
Where X is the value of interest, which is 137 in this case. So, the calculation is:
Z = (137 - 135) / 6
Z = 0.3333
Once we have the z-score, we look up this value in a standard normal distribution table (or use statistical software) to find the probability of a z-score being less than 0.3333, which corresponds to the area under the curve to the left of the z-score. We subtract this probability from 1 since we are looking for the area to the right (the percentage of males with blood pressure higher than 137).
If the standard normal distribution table indicates that the area to the left of 0.3333 is approximately 0.6293, then the area to the right (the probability of being higher than 137) is:
1 - 0.6293 = 0.3707 or 37.07%
To the nearest tenth, the percentage is 37.1%.
This method is based on the properties of the normal distribution of systolic blood pressure in males, which is a common application in statistics for determining probabilities.