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.

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:

Where and

For this case the z score given by:

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:

Where and

For this case the z score given by:

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.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for