What is the z-score of sample X, if $n=36,\text{}\mu =13.7,\text{}\text{St.Dev}=21,\text{}{\mu}_{X}=9.9$?

Yazmin Sims
2022-10-14
Answered

What is the z-score of sample X, if $n=36,\text{}\mu =13.7,\text{}\text{St.Dev}=21,\text{}{\mu}_{X}=9.9$?

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dwubiegrw

Answered 2022-10-15
Author has **13** answers

Given

$n=36\phantom{\rule{0ex}{0ex}}\mu =13.7\phantom{\rule{0ex}{0ex}}\text{St.Dev}=21\phantom{\rule{0ex}{0ex}}{\mu}_{X}=9.9$

Find the Standard Error

$SE=\frac{SD}{n}=\frac{21}{36}=0.58$

Find the z-score

$z=\frac{{\mu}_{X}-\mu}{SE}=\frac{9.9-13.7}{0.58}=-6.55$

$n=36\phantom{\rule{0ex}{0ex}}\mu =13.7\phantom{\rule{0ex}{0ex}}\text{St.Dev}=21\phantom{\rule{0ex}{0ex}}{\mu}_{X}=9.9$

Find the Standard Error

$SE=\frac{SD}{n}=\frac{21}{36}=0.58$

Find the z-score

$z=\frac{{\mu}_{X}-\mu}{SE}=\frac{9.9-13.7}{0.58}=-6.55$

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Using the standard score formula, $z=(x-\mu )/\sigma $, the z-score equals to two decimal places 1.64, which corresponds to a probability of 0.9495 on my z-score tables. However, on the answer key provided, it states the probability is 0.0505 or what would correspond to a z-score of −1.64.

Is this a trick of the wording involved in the question or are my z-tables (or standard score formula) wrong?

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I know that the answer is 1.645. But i tried to look it up on the Z score table, but i couldn't figure out how to read it. I did the following: 0.9+1 = 1.90.

I then look at the left side for 1.9 and on the top i search for 0.0, the number that is stated there is 0.9713. Which isnt true.

Can someone explain me please how to use the Z-table

I know that the answer is 1.645. But i tried to look it up on the Z score table, but i couldn't figure out how to read it. I did the following: 0.9+1 = 1.90.

I then look at the left side for 1.9 and on the top i search for 0.0, the number that is stated there is 0.9713. Which isnt true.

Can someone explain me please how to use the Z-table

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