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?
My favourite webpage for this kind of question:
http://davidmlane.com/hyperstat/z_table.html
Just enter the data and pick the "between" option
I don't know if I got it right but my answer was 0.005422 in the top calculator and for the bottom it was 0.05. Is that correct?
To find the percentage of adult males with blood pressure between 161.28 and 164.9, we need to calculate the z-scores for the given values and then find the corresponding area under the normal distribution curve.
First, we need to calculate the z-score for the lower value of 161.28.
z1 = (x1 - mean) / standard deviation
z1 = (161.28 - 138) / 9.7
z1 ≈ 2.42
Next, we calculate the z-score for the higher value of 164.9.
z2 = (x2 - mean) / standard deviation
z2 = (164.9 - 138) / 9.7
z2 ≈ 2.76
Now, we have the z-scores for both values. We can use a standard normal distribution table or a calculator to find the area between these two z-scores.
Using a standard normal distribution table, we look up the area corresponding to z = 2.42, which is approximately 0.9920. This represents the area to the left of 2.42.
Next, we look up the area corresponding to z = 2.76, which is approximately 0.9977. This represents the area to the left of 2.76.
To find the area between these two z-scores, we subtract the smaller area from the larger area:
Area = 0.9977 - 0.9920 ≈ 0.0057
Finally, we convert the area to a percentage:
Percentage = Area * 100
Percentage ≈ 0.0057 * 100 ≈ 0.57%
Therefore, approximately 0.57% of adult males have blood pressure between 161.28 and 164.9.