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.

D. The z scores are numbers without units of measurement.

Step-by-step explanation:

Z-scores are without units, or are pure numbers.

0 and 1

Step-by-step explanation:

Given that,

The distribution of certain test score is non- standard normal distribution with mean 50 and a standard deviation of 6.

we know that the

standard normal deviation has mean 0 and standard deviation 1.

So, All test scores have been standardized by converting them to z score.

mean = 0 and standard deviation= 1

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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:

[tex]X \sim N(77.5,11.6)[/tex]

Where [tex]\mu=77.5[/tex] and [tex]\sigma=11.6[/tex]

For this case the z score given by:

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

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:

[tex]X \sim N(77.5,11.6)[/tex]

Where [tex]\mu=77.5[/tex] and [tex]\sigma=11.6[/tex]

For this case the z score given by:

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

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.

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.

women

Step-by-step explanation:

because yeah that answe

b. The mean is 0 and the standard deviation is 1

Step-by-step explanation:

When the test score are standardized, they follow the standard normal distribution. The main feature of standard normal distribution is that it has zero mean and unit variance. So, when the test scores standardized by converting them to z-scores, the values of mean and standard deviation of standardized test scores are 0 and 1.

[tex]\mu=0\\\\\sigma=1[/tex]

Step-by-step explanation:

We have a normal distribution for the pulse rates of women, with mean of 77.5 beats per minute and standard deviation of 11.6 beats per minute.

We want to convert this values to the standarized normal distribution.

The z-score is defined by:

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

By definition, when we calculate the z-score, we transform any normal distribution into the standard normal distribution. This standard normal distribution has a mean of 0 and a standard deviation of 1.

This standard normal distribution enables to calculate the probabilities for any combination of parameters of the normal distribution with only one table, corresponding to the standard normal distribution probabilities.

Mean value is 0 and standard deviation is 1 after all test scores have been standardized by converting them to z-scores using z

Step-by-step explanation:

In a standard normal distribution (also called as Gaussian distribution) all values of the sample can be projected to a normal distribution with mean 0 and standard deviation 1 using their z-scores.

z-score of a value X can be calculated as follows:

z= where

50 is the mean of the test scores

6 is the standard deviation of test scores

So we need to find the P (Z< 1.0776) which is equal to 0.86 from z- tables.

Step-by-step explanation:

Given that mean = 77.5 beats per minute

Standard deviation= s= 11.6 beats per minute

We need to find the pulse rate of randomly selected women.

Suppose randomly selected women X= 90

The test statistic used here is

z = (x − μ) /σ

Putting the values we get

z= 90- 77.5/ 11.6

z= 1.0776

So we need to find the P (Z< 1.0776) which is equal to 0.86

This is a supposed values of randomly selected women. Any other value can be solved in the same way.

0 and 1

Step-by-step explanation:

Given that,

The distribution of certain test score is non- standard normal distribution with mean 50 and a standard deviation of 6.

we know that the

standard normal deviation has mean 0 and standard deviation 1.

So, All test scores have been standardized by converting them to z score.

mean = 0 and standard deviation= 1