Question

The mean diastolic blood pressure of people in the U.S. is 77 with a standard deviation of 11. Assume that diastolic blood pressure follows a normal distribution. a. What percentage of the people in the U.S. have diastolic blood pressure between 77 and 88? b. What percentage of the people in the U.S. have diastolic blood pressure between 66 and 88? c. What percentage of the people in the U.S. have diastolic blood pressure between 55 and 99? d. What percentage of the people in the U.S. have diastolic blood pressure below 55

Answer 1

a. Approximately 34.13% of people in the U.S. have diastolic blood pressure between 77 and 88.

b. Roughly 84.13% of people in the U.S. have diastolic blood pressure between 66 and 88.

c. Around 99.73% of people in the U.S. have diastolic blood pressure between 55 and 99.

d. Less than 0.15% of people in the U.S. have diastolic blood pressure below 55.

Step-by-step explanation:

a. To find the percentage of people with diastolic blood pressure between 77 and 88, we'll use the z-score formula:
`\(z = (x - \mu)/(\sigma)\)`, where (x) is the value, (mu) is the mean, and (sigma) is the standard deviation. For 77, the z-score is z= 77-77)/11, and for 88, (z = 88 - 77 /11≈ 1). Referring to the standard normal distribution table or using a calculator, the area between (z = 0) and (z = 1) is about 0.3413 or 34.13%.

b. Extending the range to include 66, we calculate the z-scores for 66 and 88: (z₆₆ = 66 - 77)/11 ≈ -1) and (z₈₈ = 88 - 77)/11≈ 1). Using the standard normal distribution table, the area between (z = -1) and (z = 1) is about 0.8413. Therefore, approximately 84.13% of people have diastolic blood pressure between 66 and 88.

c. For the range of 55 to 99, the z-scores are (z₅₅ = {55 - 77 /11≈-2) and (z₉₉ = {99 - 77 /11≈ 2). Referring to the standard normal distribution table, the area between (z = -2) and (z = 2) is approximately 0.9973 or 99.73%.

d. To find the percentage of people with diastolic blood pressure below 55, we use the z-score formula: (z₅₅ = {55 - 77 /11≈). From the standard normal distribution table, the area to the left of (z = -2\) is less than 0.15%. Hence, less than 0.15% of people have diastolic blood pressure below 55.