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September 19th, 2009, 12:19 PM   #1
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What are the steps to solve this z-score

Human body temperatures are normally distributed with a mean of 98.20 and a standard deviation of 0.62.
Find the body temperature corresponding to a z-score of z=1.73

I have no idea where to begin.
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September 21st, 2009, 02:33 PM   #2
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Re: What are the steps to solve this z-score

to understand how to derive z-score(or what is z-score) you need to understand what is meant to be z-score.

z-score is the measure of how many standard deviation away is the observation from the mean.

so if you have an observation X and you know it's mean is E[X].

Then the term X-E[X] would be the distance the observation is away from the mean and the sighs (+,-) indicates either it's to the right of the mean or the left of the mean.

from there on it's pretty easy to calculate the distance away from the mean in terms of standard deviation.

(X-E[X])/SD(X) is the number of standard deviation away from the mean of the observed data. where SD(X) is the standard deviation of X.

In your case that you have a z=1.73.

which means the original data is 1.73 standard deviation away to the right of the mean.

solve for value of X such that (X-98.20)/0.62 = 1.73 then you will obtain your original data.
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