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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?

Respuesta :

kudzordzifrancis

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;

[tex]z=\frac{x-\mu}{\sigma}[/tex] 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.

MrRoyal

The values of the mean and the standard deviation are 0 and 1, respectively while the z-score has no unit of measurement

How to determine the mean and standard deviation?

The formula of the z-score is given as:

[tex]z = \frac{x - \mu}{\sigma}[/tex]

The mean and the standard deviation are given as:

[tex]\bar x = 77.5\ \sigma = 11.6[/tex]

When the formula, [tex]z = \frac{x - \mu}{\sigma}[/tex] is applied;

We have:

[tex]\bar x = 0,\ \sigma = 1[/tex]

This means that: the values of the mean and the standard deviation are 0 and 1, respectively

The unit of the z-score?

The z-score has no units because the units of the mean and the standard deviation are the same i.e. beats per minute.

Read more about z-scores at:

https://brainly.com/question/25638875

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