The mean of a set of data is -2.14 and its standard deviation is 3.94. Find the z score for a value of 5.40?

1 Answer
Geoff K.
Apr 23, 2018

#z=1.914#

Explanation:

Given #X# is #"N"(mu=–2.14, sigma = 3.94),# we seek a value #z# such that

#"P"(X<5.40)="P"(Z < z)#

where #Z# has the standard normal distribution of #"N"(0, 1).# In other words, we seek to know how many standard deviations above (or below) the mean our value of 5.40 is in its distribution.

This value is found by "centering" our #x# value (by subtracting #mu#) and then "scaling" it (by dividing that by #sigma#):

#z=(x-mu)/sigma#

#=(5.40-(–2.14))/3.94#

#=1.914#

So our value of #x=5.40# is 1.914 standard deviations above the mean.

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