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### Course: Statistics and probability>Unit 4

Lesson 6: Normal distribution calculations

# Standard normal table for proportion below

Finding the proportion of a normal distribution that is below a value by calculating a z-score and using a z-table.

## Want to join the conversation?

• There is no proper presentation of the z-table anywhere on the curriculum of your Statistics and Probability. I guess it's a standard thing which we just have to find somewhere on our own?
• I agree that this was an oversight on KA's part not to provide a table. But I did find this resource from The University of Arizona to be useful:

https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf

It's just a PDF that has the z-table values for a standard normal distribution curve so it avoids all the pesky ads of a lot of the other sites that you might have found while trying to Google for a proper z-table.
• I paused the video before it got to using z-tables, and came up with a different answer. Darnell is +0.57 SD above the mean. 1 whole SD is 34%. 34% * 0.57 = 19.38 (%). Plus the 50% below the mean = 69.38%. I'm guessing I've made a dumb error somewhere along the way, but be great to know why this approach isn't the right one. Thanks.
• The area under the distribution curve is not proportional to the distance away from the mean, so multiplying the number of standard deviations by 0.34 gives us the wrong result.

0.57 ∙ 0.34 = 19.38%, but the correct percentage is 21.57%
• On the AP exam are you provided with a z-Table?
• I don't know about the AP exam, but in Cambridge AS and A2 they do provide you with a table.
(1 vote)
• Where does the Z-table come from?
I know how to use it. but I don't know what it is!
• The z-table is derived from the standard normal distribution, which has a mean of 0 and a standard deviation of 1. The values in the table represent cumulative probabilities for different z-scores. These values are obtained through mathematical calculations or numerical integration of the standard normal probability density function. The z-table provides a convenient way to look up probabilities associated with specific z-scores without needing to perform these calculations every time.
• Is there a Z-Table available on Khan?
• Khan doesn’t provide a z-table. You can find one by searching z-table.net
• If you need help finding a Z-Table, use this resource from the University of Arizona:

https://www.math.arizona.edu/~rsims/ma464/standardnormaltable.pdf

It's just a PDF that has the z-table values for a standard normal distribution curve. What's nice about it is that it avoids all the pesky advertisements found on a lot of the other sites that you might have come across while trying to find a proper z-table.
• I'm still confused. How do you know if you need to subtract 1-the z score? And why do you need to subtract 1 from the z score?
• In the context of cumulative probabilities, subtracting 1 from the z-score is necessary when you're interested in finding the proportion of values greater than a certain threshold rather than less than. For example, if you want to find the proportion of values greater than a specific value, you would use the complement rule, which states that Pr (X > x) = 1 − Pr (X < x), where X is a random variable and
x is a threshold value. So, by subtracting the cumulative probability from 1, you're essentially finding the proportion of values greater than the threshold.
(1 vote)
• `I know this may sound dumb but why are bell curves` `called` `bell curves`