Dear mentors!
I keep struggling trying to figure out why the z value is 1.96? The video says the following: " When a normal distribution is standardized, then 68% of the population falls one standard deviation away from the mean, whereas 95% falls two standard deviations away from the mean". Since the standard deviation = 1, doesn’t it mean, that the 95% point, which is two standard deviations away is equal to 1*2=2? if someone could please explain why is it 1.96
Thank you!
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2 standard deviations from the mean would technically be 2 as you rightly pointed out, but the critical value used in statistical tables and calculations for a 95% confidence interval is approximately 1.96 due to rounding and approximation. If you use the tables or a programming language like Python or R, you would get about 1.95996, which approximates to 1.96 or 2.
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Dear @ossovskiy,
For a 95% confidence interval, we’re looking for the Z-score that leaves 2.5% (0.025) in each tail.
Using a standard normal distribution table or a calculator, we find that the Z-score corresponding to an area of 0.025 in the upper tail is approximately 1.96. This means that the Z-score that leaves 2.5% in each tail (and thus 95% in the middle) is 1.96.
Hope this makes you clear.
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Thank you friends!
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