How to calculate the minimum and maximum length of the 6th sample, using only measurement data of the first 5 samples?

Asked Apr 09 '21 at 15:58

Active Apr 09 '21 at 16:07

Viewed 15 times

I have a sack of 1000 sticks.
The length of the sticks are normally distributed.
I randomly take out 5 sticks and measure them to be [40; 30; 60; 20; 30] mm long.
How can I now calculate, with a confidence interval of 99%, the minimum and maximum length of the sixth stick?

I have managed to calculate the population mean standard deviation accurately using t-table but it really doesn't help me here.

edited Apr 09 '21 at 16:07

asked Apr 09 '21 at 15:58

warpi

@AryaMcCarthy Yes, 99% confidence interval, thanks! – warpi Apr 09 '21 at 16:04
@Arya You don't mean a confidence interval: this is a prediction interval. The two are distinct concepts. – whuber Apr 09 '21 at 17:15
1

Oof, thanks for educating me! – Arya McCarthy Apr 09 '21 at 17:31

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