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 equals StartFraction (x minus mu )Over sigma EndFractionz= (x−μ) σ​?

Answer 1

Answer:

$\mu=0\\\\\sigma=1$

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:

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

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.