What is the z-score of sample X, if $n=256,\text{}\mu =42,\text{}\text{St.Dev}=80,\text{}{\mu}_{X}=89$?

Marcelo Maxwell
2022-09-27
Answered

What is the z-score of sample X, if $n=256,\text{}\mu =42,\text{}\text{St.Dev}=80,\text{}{\mu}_{X}=89$?

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Cremolinoer

Answered 2022-09-28
Author has **11** answers

Given

$n=256\phantom{\rule{0ex}{0ex}}\mu =42\phantom{\rule{0ex}{0ex}}\text{St.Dev}=80\phantom{\rule{0ex}{0ex}}{\mu}_{X}=89$

Find the Standard Error

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

Find the z-score

$z=\frac{89-42}{5}=9.4$

$n=256\phantom{\rule{0ex}{0ex}}\mu =42\phantom{\rule{0ex}{0ex}}\text{St.Dev}=80\phantom{\rule{0ex}{0ex}}{\mu}_{X}=89$

Find the Standard Error

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

Find the z-score

$z=\frac{89-42}{5}=9.4$

asked 2022-05-03

Trying to find the probability $b/w$ two scores. I know mapping to $z$-score is:

${z}_{11}=(11-10)/1.5=.67$

and

${z}_{14}=(14-10)/1.5=2.67$

So,

$\overline{x}=10,\text{}\sigma =\mathrm{1.5.}$

Would I simple subtract the two from each other? and so on the real number line it would range from 0 to 100 and that is how the distribution would be set up. So, 2.67−2=2?

On the z-table 2 is given a value of 0.9772.

My teacher likes to give things as either a proportion or a percentage so how might one be able to address the two. Like if this question was asking for the proportion of scores that fall between 11 and 14 or if the question said what's the percentage of scores that fall between 11 and 14. How might be able to address both scenarios?

Just confused on the ideas of proportion, probability, and percentage and how they are relate.

${z}_{11}=(11-10)/1.5=.67$

and

${z}_{14}=(14-10)/1.5=2.67$

So,

$\overline{x}=10,\text{}\sigma =\mathrm{1.5.}$

Would I simple subtract the two from each other? and so on the real number line it would range from 0 to 100 and that is how the distribution would be set up. So, 2.67−2=2?

On the z-table 2 is given a value of 0.9772.

My teacher likes to give things as either a proportion or a percentage so how might one be able to address the two. Like if this question was asking for the proportion of scores that fall between 11 and 14 or if the question said what's the percentage of scores that fall between 11 and 14. How might be able to address both scenarios?

Just confused on the ideas of proportion, probability, and percentage and how they are relate.

asked 2022-07-17

A successful basketball player has a height of 6 feet 2 inches, or 188 cm. Based on statistics from a data set, his height converts to the z score of 1.95. How many standard deviations is his height above the mean?

The player's height is [_] standard deviation(s) above the mean. (Round to two decimal places as needed.)

The player's height is [_] standard deviation(s) above the mean. (Round to two decimal places as needed.)

asked 2022-08-19

in some exam past papers I have been doing I have come across the statistics equation

z=(sample mean - mean)/standard deviation

as well as the equation

z = (sample mean - mean)/(standard deviation/sqrt n).

could anyone please explain when to use which equation and what the difference is? thanks so much!

z=(sample mean - mean)/standard deviation

as well as the equation

z = (sample mean - mean)/(standard deviation/sqrt n).

could anyone please explain when to use which equation and what the difference is? thanks so much!

asked 2022-10-24

I want to apply to a university where the 25th /75th percentiles for the SAT Math are 490 / 620 respectively, but I am curious how would I find the mean and the standard deviation assuming that the data is normally distributed? I know that we are talking about the middle 50th-percentile and ${z}_{0.25}=620$ and ${z}_{0.75}=490$

asked 2022-08-13

People with z-scores above 2.5 on an IQ test are sometimes classified as geniuses. If IQ scores have a mean of 100 and a standard deviation of 16 points, what IQ score do you need to be consideblack a genius?

asked 2022-07-20

Transforming an entire distribution of scores into z-scores changes an originally positively skewed distribution to a negatively skewed z-score distribution. True or False

asked 2022-07-23

What is the z-score of sample X, if $n=9,\mu =56,SD=30,\phantom{\rule{1ex}{0ex}}\text{and}\phantom{\rule{1ex}{0ex}}E\left[X\right]=32$?