The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 119 and standard deviation of 18 .
Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher.
a. Around what percentage of adults in the USA have stage 2 high blood pressure?
b. If you sampled 3500 people, how many would you expect to have BP> 160? Give your answer to the nearest person.
people
c. Stage 1 high BP is specified as systolic BP between 140 and 160. What percentage of adults in the US qualify for stage 1?
This is an example of why some questions go unanswered.
Rather than post a question and learn how to solve it, a student posts a whole homework assignment, with no indication of any effort or work, and expects someone to go through a dozen questions, do all the work, and hand out all the answers. Good luck with that.
To answer these questions, we can use the properties of the normal distribution. Let's go through each question step-by-step:
a. To find the percentage of adults in the USA with stage 2 high blood pressure (systolic BP ≥ 160), we need to calculate the area under the normal curve to the right of 160.
First, we need to convert the systolic blood pressure to a z-score using the formula:
z = (x - μ) / σ
where x is the value (160), μ is the mean (119), and σ is the standard deviation (18).
z = (160 - 119) / 18 ≈ 2.278
Next, we look up the z-score in a standard normal table or use a calculator to find the corresponding area. The area to the right of 2.278 is approximately 0.0114.
To find the percentage, we multiply this value by 100 to get:
Percentage = 0.0114 * 100 ≈ 1.14%
Therefore, approximately 1.14% of adults in the USA have stage 2 high blood pressure.
b. To determine how many people out of a sample of 3500 would have a systolic blood pressure greater than 160, we need to find the corresponding area under the normal curve.
Using the z-score formula again, we find that z = (160 - 119) / 18 ≈ 2.278.
Now, we can use the z-score and the standard normal table (or a calculator) to find the area to the right of 2.278. Let's denote this area as A.
A ≈ 0.0114
To find the number of people expected to have a systolic blood pressure greater than 160 out of a sample of 3500, we multiply A by the sample size:
Number of people = A * Sample size
Number of people ≈ 0.0114 * 3500 ≈ 39.9 (rounded to the nearest person)
Therefore, we would expect approximately 40 people to have systolic blood pressure greater than 160 out of a sample of 3500.
c. To find the percentage of adults in the USA who qualify for stage 1 high blood pressure (systolic BP between 140 and 160), we need to calculate the area under the normal curve between these values.
First, we need to convert the systolic blood pressure limits to z-scores using the formula:
z = (x - μ) / σ
For 140:
z1 = (140 - 119) / 18 ≈ 1.167
For 160:
z2 = (160 - 119) / 18 ≈ 2.278
Next, we find the corresponding areas to the left of these z-scores using the standard normal table or a calculator. Let's denote these areas as A1 and A2, respectively.
A1 ≈ 0.877
A2 ≈ 0.9886
Now, to find the percentage of adults in the USA who qualify for stage 1 high blood pressure, we subtract A1 from A2 and multiply by 100:
Percentage = (A2 - A1) * 100
Percentage ≈ (0.9886 - 0.877) * 100 ≈ 11.86%
Therefore, approximately 11.86% of adults in the USA qualify for stage 1 high blood pressure.