Can you please explain to me you the numbers in denoted in the confidence intervals derived?
For example when getting a 95% confidence interval for the mean we use 1.96 because in a normal distribution 95% of the values lie in the interval from 1.96 standard deviations below the mean to 1.96 standard deviations above the mean.
Do you know where they 1.96 initially came from? The question in my book acknowledges all of the percentiles with the confidence intervals but specifically asks how these numbers (1.645, 1.96, 2.33, 2.567) were selected.
They come from the normal distribution as explained in post #2.
Have a look here Z table - Normal Distribution
You should find that 1.645 is the 90th percentile, 1.96 the 95th, 2.33 the 98th, 2.567 the 99th percentile
Yes, I understand exactly what you are saying but the question wants to know where those numbers originated when the equation was being developed in the original development of this equation. In other words, how did the founder of the equation decide on those particular numbers? Sounds like a crazy question but it's the one I've been given.
I'm sorry that it appears I don't understand. I know what you're saying exactly but the question wants to know how these numbers were originally selected by the person who made up this equation. Were the numbers pulled out of the air or were they based on something? It's more a history question I think than math.