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# Finding z-score for a percentile

In any normal distribution, we can find the z-score that corresponds to some percentile rank. If we're given a particular normal distribution with some mean and standard deviation, we can use that z-score to find the actual cutoff for that percentile. In this example, we find what pulse rate represents the top 30% of all pulse rates in a population.

## Want to join the conversation?

• Can someone explain why the z score of 0.53 was used instead of 0.52?
0.52 differed from the ideal value by 0.0015 instead of 0.0019 so it seems like that would have been a better choice. I realize that both give the same answer when rounded to one heartbeat per minute but it still seems odd.
• I don't agree to the 0.53 either. The question doesn't state whether she wants at least the top 30% or at max the top 30%, but the former seems reasonable. Choosing 0.53 as the z-value, would mean we 'only' test 29.81% of the students.

I would have assumed it would make more sense to choose z=0.52 for that reason, so that we at least cover 30%.
• it would be helpful to show the formula manipulation to get to the answer
• z = (x - µ)/ σ

So in video's example,
0.53 = (x - µ)/ σ
0.53 * 11 = x - µ
4.77 + µ = x
x = 84.77
• What's the spreadsheet formula to find the exact z score of a given percentage?
In the video, at we that the percentage=0.7019 so the z score=0.5 (but we actually want the z score of a 0.7)
• The exact z score for a given cumulative percentage, in Excel in Office 365, is either
=NORMSINV(percentage)
or
=NORM.S.INV(percentage)

So the exact z score for a cumulative percentage of 0.7 is either
=NORMSINV(0.7)
or
=NORM.S.INV(0.7)

Have a blessed, wonderful day!
• How did you know it had to be at least 70% ?
• Where do you find the z-score table
• http://www.z-table.com/
You are able to find z-score table on this website :)
• Can someone explain how to get .52 if you aren't given a table?

I am taking a teaching test soon and we won't be given a table.

Thanks
• Are you sure? There is no way to do it by hand. The only ways are to use the table or use a calculator.
• How do you find the mean and standard deviation given a percentile and a value? For example, if you are given that 16 is the 25th percentile and 40 and the 97.5% for a normal distribution.
• Where can I get a down load of the z-scores?