Question

Pulse rates of women are normally distributed with a mean of 77.5 beats per minute and a standard deviation of 11.6 beats per minute.
a)What are the values of the mean and standard deviation after converting all pulse rates of women to z-scores using z=(x−μ)/σ?


b)The original pulse rates are measured with units of "beats per minute." What are the units of the corresponding z-scores?

Answer 1

Answer:

a) Mean=0 and Standard deviation=1

b) The z-scores have no units of measurement

Step-by-step explanation:

When we convert all the pulse rates of women to z-scores using the formula;

$z=\frac{x-\mu}{\sigma}$ the mean is 0 and the standard deviation is 1.

The reason is that, the resulting distribution of z-scores forms a normal distribution which has a mean of 0 and a standard deviation of 1.

b) The z-scores are standardize scores and has no units of measurement. They give us how many standard deviations below or above the mean of the corresponding values.