Question

for a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 32 beats per minute, the mean of the listed pulse rates is \\( \bar { x } = 7 3. 0 \\) beats per minute, and their standard deviation is \\( s = 1 6. 1 \\) beats per minute.
a. what is the difference between the pulse rate of 32 beats per minute and the mean pulse rate of the females?
b. how many standard deviations is that the difference found in part (a)?
c. convert the pulse rate of 32 beats per minutes to a z score.
d. if we consider pulse rates that convert to z scores between - 2 and 2 to be neither significantly low nor significantly high, is the pulse rate of 32 beats per minute significant?
a. the difference is 41 beats per minute.
(type an integer or a decimal. do not round.)
b. the difference is \\( \square \\) standard deviations.
(round to two decimal places as needed.)

Explanation:

Step1: Calculate the difference

The formula for the difference is \( \text{Difference}=\bar{x}-x\). Given \(\bar{x} = 73.0\) and \(x = 32\), then \( \text{Difference}=73.0 - 32=41\) beats per minute.

Step2: Calculate the number of standard deviations

The formula for the number of standard deviations is \(n=\frac{\text{Difference}}{s}\). Substitute \(\text{Difference} = 41\) and \(s = 16.1\) into the formula: \(n=\frac{41}{16.1}\approx2.55\) standard deviations.

Step3: Calculate the z - score

The z - score formula is \(z=\frac{x-\bar{x}}{s}\). Substitute \(x = 32\), \(\bar{x}=73.0\) and \(s = 16.1\) into the formula: \(z=\frac{32 - 73.0}{16.1}=\frac{- 41}{16.1}\approx - 2.55\)

Step4: Determine significance

Since \(|z|=2.55>2\), the pulse rate of 32 beats per minute is significantly low.

Answer:

a. 41 beats per minute
b. \(2.55\) standard deviations
c. \(z\approx - 2.55\)
d. Yes, the pulse rate of 32 beats per minute is significantly low.