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. Answer the following questions. What are the values of the mean and standard deviation after converting all pulse rates of women to z scores using z = (x - mu )/sigma ? mu = sigma = The original pulse rates are measure with units of "beats per minute". What are the units of the corresponding z scores? Choose the correct choice below. The z scores are measured with units of "beats per minute". The z scores are measured with units of "minutes per beat". The z scores are measured with units of "beats." The z scores are numbers without units of measurement.

Answer 1

Answer:

Let X the random variable that represent the pulse rates of a population, and for this case we know the distribution for X is given by:

$X \sim N(77.5,11.6)$  

Where $\mu=77.5$ and $\sigma=11.6$

For this case the z score given by:

$z=\frac{x-\mu}{\sigma}$

And for this case the z score is without units, so the correct answer would be:

The z scores are numbers without units of measurement.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Solution to the problem

Let X the random variable that represent the pulse rates of a population, and for this case we know the distribution for X is given by:

$X \sim N(77.5,11.6)$  

Where $\mu=77.5$ and $\sigma=11.6$

For this case the z score given by:

$z=\frac{x-\mu}{\sigma}$

And for this case the z score is without units, so the correct answer would be:

The z scores are numbers without units of measurement.