Question

To qualify for a medical study, an applicant must have a systolic blood pressure in the 80% of the middle range. If the systolic blood pressure is normally distributed with a mean of 120 and a standard deviation of 4, what are the upper and lower limits of blood pressure a person must have to qualify for the study?

a. Lower limit: 108, Upper limit: 132
b. Lower limit: 112, Upper limit: 128
c. Lower limit: 116, Upper limit: 124
d. Lower limit: 120, Upper limit: 120

Answer 1

To qualify for the medical study, an applicant must have a systolic blood pressure in the 80% of the middle range. Using the normal distribution, the lower limit is approximately 116 and the upper limit is approximately 124.

Step-by-step explanation:

To qualify for the medical study, an applicant must have a systolic blood pressure in the 80% of the middle range. Since the systolic blood pressure is normally distributed with a mean of 120 and a standard deviation of 4, we can use the standard normal distribution to find the z-scores corresponding to the lower and upper limits of the blood pressure range. The lower limit is found by subtracting the z-score for the 80th percentile from the mean, and the upper limit is found by adding the z-score for the 80th percentile to the mean. Using the z-table or calculator, the z-score for the 80th percentile is approximately 0.845.

Therefore, the lower limit is 120 - (0.845 * 4) = 116.42,

approximated to 116, and the upper limit is 120 + (0.845 * 4) = 123.58, approximated to 124.

Therefore, the correct answer is c. Lower limit: 116, Upper limit: 124.