Question #3c68b

2 Answers
namralos
May 6, 2017

A z-score is a multiple of the Std. Dev. for a standard normal distribution.

Explanation:

The standard deviation of any distribution measures how spread out ("dispersed") the scores are.

For any normal distribution, expect approximately 68% of the data to lie within 1 standard deviation of the mean. Expect about 95% to lie within 2 standard deviations of the mean. Expect 99.7% to lie within 3 standard deviations of the mean.

For a standard normal curve, a z-score indicates the number of standard deviations that a given score is above or below the mean for that distribution. The z-score does not identify the standard deviation of the original distribution, but for the standard normal distribution the standard deviation is sigma = 1σ=1.

Nallasivam V
May 7, 2017

Standard distribution is calculated for a given distribution,
z-score is calculated for an xx value of a given distribution.

sigma = 6.67σ=6.67

Explanation:

Standard distribution is calculated for a given distribution,
z-score is calculated for an xx value of a given distribution.

For each xx value in the given distribution, there is one corresponding zzscore.

There are as many zscores as there are zscoresastherearex# values. But there is only one standard deviation value.

SD along with the mean of a series is used to calculate zz score of a given xx value.

Given -
Mean barx=45¯x=45
An element of this data set x=50x=50

z=0.75z=0.75
sigma=σ=?

z=(x-barx)/(sigma)z=x−¯xσ
0.75=(50-45)/sigma0.75=50−45σ
0.75sigma=50-450.75σ=50−45
sigma =5/0.75=6.67σ=50.75=6.67

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