Question

A study has estimated at 99.5% confidence level, the pulse rates of adult males to be between 67 bpm and 85 bpm, after randomly selecting 149 subjects.

: a) Find the population standard deviation used for this study. he standard deviation is (round this result to 1 decimal place as needed.)

Answer 1

To find the population standard deviation (σ), use the margin of error from the confidence interval and the z-score corresponding to the 99.5% confidence level. The standard deviation is calculated to be approximately 4.6 bpm.

Step-by-step explanation:

The student's question involves calculating the population standard deviation given a confidence interval, sample size, and confidence level (which is related to the concept of z-scores for normal distribution). To find the population standard deviation (σ), we use the formula for the confidence interval of the mean for a normally distributed population:

CI = ± z * (σ/√N)

Here, CI is the margin of error, z is the z-score corresponding to the confidence level, σ is the population standard deviation, and N is the sample size.

For a 99.5% confidence level, the z-score is approximately 2.807. We have the following margin of error (half the width of the confidence interval) for the pulse rates:

CI = (85 - 67)/2 bpm = 9 bpm

Using the formula:

9 = 2.807 * (σ/√149)

σ = 9/(2.807/√149)

Solving for σ gives us:

σ ≈ 4.6 bpm (rounded to one decimal place).

Therefore, the population standard deviation used in the study is approximately 4.6 bpm.