Answer to Question #238767 in Statistics and Probability for Nana

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 x=72.0 beats per​ minute, and their standard deviation is s=10.7 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?

Answer 1

Let x₀ be the lowest pulse rate =39

s is the sample standard deviation=10.7

$x(bar)$ the sample mean=72.0

a.

The difference is given by,

x₀ -$x(bar)$

39-72.0=-33

b.

number of standard deviations is given by,

=|x₀ -$x(bar)$|/s

=|39-72.0|/10.7

=|-33|/10.7

=33/10.7

=3.08(2 decimal places)

Therefore, the lowest pulse rate is 3.08 standard deviations below the mean.

c.

The Z score is given as,

Z = (x₀-$x(bar)$) /s

=(39-72.0)/10.7

=-33/10.7

=-3.08(2 decimal places)

d.

If we consider pulse rates that convert to Z scores between -2 and 2, then -3.08 is not within this range hence, the pulse rate of 39 beats per minute is significantly low.