What is the z-score of sample X, if $n=196,\text{}\mu =55,\text{}\text{St.Dev}=42,\text{}{\mu}_{X}=58$?

Matias Aguirre
2022-07-16
Answered

What is the z-score of sample X, if $n=196,\text{}\mu =55,\text{}\text{St.Dev}=42,\text{}{\mu}_{X}=58$?

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LitikoIDu6

Answered 2022-07-17
Author has **10** answers

Given

$n=196\phantom{\rule{0ex}{0ex}}\mu =55\phantom{\rule{0ex}{0ex}}\text{St.Dev}=42\phantom{\rule{0ex}{0ex}}{\mu}_{X}=58$

Find the Standard Error

$SE=\frac{\sigma}{\sqrt{n}}=\frac{42}{\sqrt{196}}=3$

Find the z-score

$z=\frac{55-58}{3}=-0.75$

$n=196\phantom{\rule{0ex}{0ex}}\mu =55\phantom{\rule{0ex}{0ex}}\text{St.Dev}=42\phantom{\rule{0ex}{0ex}}{\mu}_{X}=58$

Find the Standard Error

$SE=\frac{\sigma}{\sqrt{n}}=\frac{42}{\sqrt{196}}=3$

Find the z-score

$z=\frac{55-58}{3}=-0.75$

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