# Question #3c68b

##### 2 Answers

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

Standard distribution is calculated for a given distribution,

z-score is calculated for an

#sigma = 6.67#

#### Explanation:

Standard distribution is calculated for a given distribution,

z-score is calculated for an

For each

There are as many

SD along with the mean of a series is used to calculate

Given -

Mean

An element of this data set

#z=0.75#

#sigma=# ?

#z=(x-barx)/(sigma)#

#0.75=(50-45)/sigma#

#0.75sigma=50-45#

#sigma =5/0.75=6.67#