Question

for a data set of the pulse rates for a sample of adult females, the lowest pulse rate is 36 beats per minute, the mean of the listed pulse rates is x = 75.0 beats per minute, and their standard deviation is s = 23.8 beats per minute.
a. what is the difference between the pulse rate of 36 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 36 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 36 beats per minute significant?
a. the difference is □ beats per minute. (type an integer or a decimal. do not round.)

Explanation:

Step1: Calculate difference in pulse rates

The mean $\bar{x}=75.0$ and the given pulse rate $x = 36$. The difference is $\bar{x}-x$.
$75.0 - 36=39.0$

Step2: Calculate number of standard - deviations

The number of standard deviations $n=\frac{\bar{x}-x}{s}$, where $s = 23.8$. So $n=\frac{39.0}{23.8}\approx1.64$.

Step3: Calculate z - score

The z - score formula is $z=\frac{x-\bar{x}}{s}$. Substituting $x = 36$, $\bar{x}=75.0$ and $s = 23.8$, we get $z=\frac{36 - 75.0}{23.8}=\frac{- 39.0}{23.8}\approx - 1.64$.

Step4: Determine significance

Since the z - score $z\approx - 1.64$ and $-2< - 1.64<2$, the pulse rate of 36 beats per minute is neither significantly low nor significantly high.

Answer:

a. 39.0
b. Approximately 1.64
c. Approximately - 1.64
d. No