vasorasy8

2022-07-06

In a given population, a score of X= 88 corresponds to z= +2.00 and a score of X= 79 corresponds to z= -1.00. Find the mean and standard deviation for the population.

I know how to find X and z-scores as well as how to plug things into the z-score formula, but I'm not sure how to solve this one. It says to sketch out a distribution table and find where the mean and SD fall on it, but I'm not sure how to do that.

I know how to find X and z-scores as well as how to plug things into the z-score formula, but I'm not sure how to solve this one. It says to sketch out a distribution table and find where the mean and SD fall on it, but I'm not sure how to do that.

Jordan Mcpherson

Beginner2022-07-07Added 16 answers

A z score is just a way of saying that it's that many standard deviations above or below the mean. Since they've given you two values and the z scores you can figure it out. Let $m,s$ denote the mean and standard deviation of the distribution. Then,

${X}_{1}-{X}_{2}=9={z}_{1}-{z}_{2}=3s$

So the $s=3$ and $m={X}_{1}-2s=82$.

${X}_{1}-{X}_{2}=9={z}_{1}-{z}_{2}=3s$

So the $s=3$ and $m={X}_{1}-2s=82$.

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