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 ​? nothing nothing 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. A. The z scores are measured with units of​ "minutes per​ beat." B. The z scores are measured with units of​ "beats per​ minute." C. The z scores are measured with units of​ "beats." D. The z scores are numbers without units of measurement.

Answer 1

(1) 0 and 1

(2) Correct option D

Explanation:

It is provided that 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.

Let X denote the pulse rates of women.

(1)

Let us consider a random variable, X that follows N (µ, σ²), then
`Z=(X-\mu)/(\sigma)`, is a standard normal variate with mean, E (Z) = 0 and variance V (Z) = 1.

That is, Z follows N (0, 1).

In statistics, a standardized score is the number of standard deviations an observation or data point is from the mean.

Thus, z-scores are a type of standardized scores.

The values of the mean and standard deviation after converting all pulse rates of women to z scores are 0 and 1 respectively.

(2)

The z scores are numbers without units of measurement.