What is the z-score of sample X, if $n=256,\text{}\mu =17,\text{}\text{St.Dev}=80,\text{}{\mu}_{X}=22$?

Jamarcus Lindsey
2022-10-08
Answered

What is the z-score of sample X, if $n=256,\text{}\mu =17,\text{}\text{St.Dev}=80,\text{}{\mu}_{X}=22$?

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Branson Perkins

Answered 2022-10-09
Author has **7** answers

Given

$n=256\phantom{\rule{0ex}{0ex}}\mu =17\phantom{\rule{0ex}{0ex}}\text{St.Dev}=80\phantom{\rule{0ex}{0ex}}{\mu}_{X}=22$

Find the Standard Error

$SE=\frac{\sigma}{\sqrt{n}}=\frac{80}{\sqrt{256}}=5$

Find the z-score

$z=\frac{17-22}{5}=-1$

$n=256\phantom{\rule{0ex}{0ex}}\mu =17\phantom{\rule{0ex}{0ex}}\text{St.Dev}=80\phantom{\rule{0ex}{0ex}}{\mu}_{X}=22$

Find the Standard Error

$SE=\frac{\sigma}{\sqrt{n}}=\frac{80}{\sqrt{256}}=5$

Find the z-score

$z=\frac{17-22}{5}=-1$

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