z-scores can be used to identify ?, ?, ? values.

Reeves 2021-10-04 Answered
z-scores can be used to identify ?, ?, ? values.

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grbavit
Answered 2021-10-05 Author has 16633 answers
Step 1
Standard normal distribution:
The normal distribution has mean as 0 and standard deviation as 1.
The total area under the density curve is equal to 1.
Let, the random variable X represents the pulse rates of women.
The z score formula is used to convert a normal distribution to a standard normal distribution.
That is, when all the X values are converted into z-scores, they get standardized and have the mean 0 and the standard deviation 1.
Hence, when all the pulse rates are converted to z-scores, the mean is 0 and the standard deviation is 1.
Step 2
The three major uses of z-scores are given as follows:
To describe the relative standing of each score:
Z-score indicates the position of a particular data value in a normal curve from the mean.
The larger the z-score value, the farther the distance of the data from the mean, whereas, the smaller the z-score, the shorter the distance of the data from the mean.
The negative value of z-score indicates that the data is below the mean, whereas, the positive value of z-score indicates that the data is above the mean.
For comparing data set:
The two different distributions of data can be easily compared by transforming the data to z-scores. Thus, it helps to compare the data sets.
Computation of relative frequency:
The relative frequency is computed using the proportion of total area under a normal bell-shaped curve. Based on the position of data on the curve, the proportion of area beyond z-score can be obtained. Thus, the relative frequency will be computed using z-score.
Step 3
Therefore, the z-score can be used to identify,
-Position of a particular data value in a bell-shaped curve.
-comparing data set
-relative frequency,
Thus, z-scores can be used to identify the position, comparison, probability values.
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