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?
Find the number of standard deviations from the mean (above) for each of the limits. For example, (161.28-138)/9.7 = 2.4
So look up the normal distribution table and find the fraction (out of 1) that is between the two limits, +2.4 σ and +____ σ.
Change the fraction to percent.
Is the answer 5%?
Yes, that is correct, well done.
It would be nice if you could get a more accurate table to get a number like 5.x%.
To find the percent 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 standard normal distribution and convert the given values to z-scores.
Step 1: Convert the given blood pressure values to z-scores using the formula:
z = (x - μ) / σ
where z is the z-score, x is the given value, μ is the mean, and σ is the standard deviation.
For the lower value, x = 161.28, μ = 138, and σ = 9.7:
z1 = (161.28 - 138) / 9.7
For the upper value, x = 164.9:
z2 = (164.9 - 138) / 9.7
Step 2: Look up the area under the standard normal distribution curve between the two z-scores calculated in Step 1. This can be done using a z-table or a calculator.
Step 3: Calculate the percent by subtracting the lower area from the higher area and multiplying by 100.
Percent = (higher area - lower area) * 100
By following these steps, you will find the percent of adult males with blood pressure between 161.28 and 164.9.