Question

The mean diastolic blood pressure for a random sample of 60 people was 84 millimeters of mercury. If the standard deviation of individual blood pressure readings is known to be 10 millimeters of mercury, find a 90% confidence interval for the true mean diastolic blood pressure of all people. Then complete the table below.

What is the lower limit of the 90% confidence interval?
What is the upper limit of the 90% confidence interval?

Answer 1

Confidence interval is used to calculate a range of values for the unknown population parameters with some level of confidence.

Here we need to find the confidence interval of the population mean. Since n > 60 and it is mentioned that the standard deviation of individual blood pressure readings is known which the pop SD we will use the normal distribution to get the interval.

n = 60   = 84 = 10

(1- )% is the confidence interval for population mean

Where = 1-90% = 10%

Therefore the C.V. =

=

= 1.6449 ..........using normal percentage tables

Margin of error =

=1.6545

The interval : (82.3455, 85.6545)

We are 90% confident that the true mean diastolic blood pressure lies within this interval.