Math Problem Statement

The mean diastolic blood pressure for a random sample of 60 people was 80 millimeters of mercury. If the standard deviation of individual blood pressure readings is known to be 11 millimeters of mercury, find a 95% confidence interval for the true mean diastolic blood pressure of all people. Then give its lower limit and upper limit. Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. (If necessary, consult a list of formulas.)

Solution

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Math Problem Analysis

Mathematical Concepts

Statistics
Confidence Intervals
Normal Distribution

Formulas

Confidence Interval: \( \bar{x} \pm z_{\alpha/2} \times \left(\frac{\sigma}{\sqrt{n}}\right) \)
Standard Error: \( SE = \frac{\sigma}{\sqrt{n}} \)
Margin of Error: \( MOE = z_{\alpha/2} \times SE \)

Theorems

Central Limit Theorem

Suitable Grade Level

Grades 11-12, College Level