Question

The diastolic pressure among 20 to 30 year olds is roughly normal. If 10 percent have levels above 86 mmHg, and 20 percent have levels below 69mmHg, what is the mean of this distribution

Answer 1

The mean of the distribution cannot be determined with the given 10th and 20th percentile values alone, as further data on the standard deviation or specific percentile values is necessary.

Step-by-step explanation:

To determine the mean diastolic blood pressure for 20 to 30 year olds in this distribution, we must recognize that a normal distribution is symmetric about its mean. Given that 10 percent have levels above 86 mmHg, which marks the upper tail of the distribution, we can infer that the 90th percentile is at 86 mmHg. Similarly, with 20 percent below 69 mmHg, the 20th percentile is at 69 mmHg. The mean of the distribution should be at the 50th percentile, which is equidistant from either end of a normal distribution. However, without additional information on the standard deviation or specific percentile values besides the 10th and 20th percentiles, it is impossible to accurately calculate the mean of this distribution. Therefore, further data would be required to provide a final answer .

Answer 2

The exact mean diastolic pressure cannot be determined from the information provided because additional data such as standard deviation or numerical percentile values are required. The typical diastolic pressure amongst young adults is approximately 80 mm Hg, which offers an educated estimation for the mean.

Step-by-step explanation:

To determine the mean diastolic pressure of a distribution that is roughly normal, we can use properties of the normal distribution and the given percentiles. In a normally distributed data set, we know that approximately 10 percent of the values lie above a certain value if that value is at the 90th percentile. Similarly, 20 percent of the values lie below a certain value if that value is at the 20th percentile.

However, to find the exact mean, we need more information such as the standard deviation or the actual numerical values for the percentiles themselves. Without this information, we can't calculate the mean exactly. Thus, with only the information provided (10 percent above 86 mmHg and 20 percent below 69 mmHg), we cannot give a specific numerical value for the mean diastolic pressure.

Since the typical diastolic pressure of a young adult is about 80 mm Hg, we can make an educated guess that in the given distribution, the mean might be close to this value, but without additional data, this remains an assumption rather than a calculation.