Answer:
[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.
The standardized value of the mean and standard deviation in a normal distribution are 0 and 1 respectively.
Since the distibution is said to be normal, applying the standardization formula will give a mean value of 0 for the pilse rate and a standard deviation value of 1.
The Zscore will the give the number of standard deviations a certain pulse rate value is above or below the mean of the distribution.
Therefore, the standardized values of the mean and standard deviation in a normal distribution is 0 and 1 respectively.
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