Question

for a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 39 beats per minute, the mean of the listed pulse rates is \\( \overline { x } = 72.0 \\) beats per minute, an standard deviation is \\( s = 10.6 \\) beats per minute.
a. what is the difference between the pulse rate of 39 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 39 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 39 beats per minute significant?
a. the difference is 33 beats per minute.
(type an integer or a decimal. do not round.)
b. the difference is 3.11 standard deviations.
(round to two decimal places as needed.)
c. the z score is \\( z = \square \\).
(round to two decimal places as needed.)

Explanation:

Step1: Recall the formula for z - score

The formula for the z - score is \(z=\frac{x-\bar{x}}{s}\), where \(x\) is the data value, \(\bar{x}\) is the mean, and \(s\) is the standard deviation.

Step2: Substitute the given values into the formula

We are given that \(x = 39\), \(\bar{x}=72.0\), and \(s = 10.6\).

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Step3: Calculate the value of z

\(z=\frac{-33}{10.6}\approx - 3.11\)

Answer:

\(z\approx - 3.11\)