What is the z-score of sample X, if $n = 36, μ = 8, S t . D e v . = 9, and μ_{X} = 11.2$ $n = 36, mu= 8, St. Dev. =9, and mu_X =11.2$ ?

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Answer 1 · 2016-06-27T06:14:06

$z = - 2.13$ $z=-2.13$

Given -

$n = 36$ $n=36$
$μ = 8$ $mu=8$
$σ = 9$ $sigma=9$
$μ_{x} = 11.2$ $mu_x=11.2$

Find the Standard Error
SE $= \frac{σ}{\sqrt{n}} = \frac{9}{\sqrt{36}} = \frac{9}{6} = 1.5$ $=sigma/sqrtn=9/sqrt36=9/6=1.5$

Find the $z$ $z$ score

$z = \frac{μ - μ_{x}}{S E} = \frac{8 - 11.2}{1.5} = \frac{- 3.2}{1.5} = - 2.13$ $z=(mu-mu_x)/(SE)=(8-11.2)/1.5=(-3.2)/1.5=-2.13$

What is the z-score of sample X, if n=36,μ=8,St.Dev.=9,andμX=11.2n = 36, mu= 8, St. Dev. =9, and mu_X =11.2?