The systolic blood pressures of a group of 18-year-old women are normally distributed with a
mean of 120 mmHg and a standard deviation of 12 mmHg. What percentage of women in this
group have a systolic blood pressure between 108 mmHg and 132 mmHg?
Play around with Z table stuff at
http://davidmlane.com/hyperstat/z_table.html
To find the percentage of women in this group with a systolic blood pressure between 108 mmHg and 132 mmHg, we need to use the concept of the standard normal distribution.
1. Convert the given values to standard units: To do this, we need to calculate the z-scores for the given values using the formula z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.
- For x = 108 mmHg: z1 = (108 - 120) / 12 = -1
- For x = 132 mmHg: z2 = (132 - 120) / 12 = +1
2. Look up the corresponding areas under the standard normal distribution curve for the calculated z-scores.
- Using a standard normal distribution table or a calculator, we find that the area to the left of z = -1 is approximately 0.1587, and the area to the left of z = 1 is approximately 0.8413.
3. Calculate the percentage between the two z-scores.
- Subtract the smaller area from the larger area: 0.8413 - 0.1587 = 0.6826
4. Multiply the result by 100 to get the percentage.
- 0.6826 * 100 = 68.26%
Therefore, approximately 68.26% of women in this group have a systolic blood pressure between 108 mmHg and 132 mmHg.