Question #3c68b

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#.

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#