My favourite webpage for this kind of question:
http://davidmlane.com/hyperstat/z_table.html
Just enter the data and pick the "between" option
http://davidmlane.com/hyperstat/z_table.html
Just enter the data and pick the "between" option
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.