Question

Question #3c68b

Answer 1

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 = 1`.

Answer 2

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

`sigma = 6.67`

Explanation:

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

For each `x` value in the given distribution, there is one corresponding `z`score.

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

SD along with the mean of a series is used to calculate `z` score of a given `x` value.

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

`z=0.75`
`sigma=`?

`z=(x-barx)/(sigma)`
`0.75=(50-45)/sigma`
`0.75sigma=50-45`
`sigma =5/0.75=6.67`