Answered

In a study of 205 adults, the mean heart rate was 75 beats per minute. Assume the population of heart rates is known to be approximately normal with a standard deviation of 8 beats per minute. What is the 95% confidence interval for the mean beats per minute?

A73.9 − 76.1
B73.7 − 76.1
C73.9 − 76.3
D70.9 − 73.3

Verified Answer :

RhondaSommer

I believe that the answer is A. :) Hope this helps!

Answer:

73.9-76.1

Step-by-step explanation:

Given : \(\bar{x} = 75\)

            \(\sigma = 8\)

            \(n = 205\)

To Find: What is the 95% confidence interval for the mean beats per minute?


Solution:

Formula : \(\bar{x}\pm z\frac{\sigma}{\sqrt{n}}\)

z = 1.96 at  95% confidence interval

Substitute the values in the formula:

\(75 \pm 1.96\frac{8}{\sqrt{205}}\)

\(75 -1.96\frac{8}{\sqrt{205}},75 0+1.96\frac{8}{\sqrt{205}}\)

\(73.9,76.1\)

Hence the 95% confidence interval for the mean beats per minute is 73.9-76.1

Thus Option A is true.

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