A box of tickets has an average of $100,$ and an SD of $20 .$ Four hundred draws will be made at random with replacement from this box. (a) Estimate the chance that the average of the draws will be in the range 80 to $120 .$ (b) Estimate the chance that the average of the draws will be in the range 99 to $101 .$
Added by Laura M.
Step 1
Since the draws are made with replacement, they are independent, and the standard deviation of the average is the standard deviation of a single draw divided by the square root of the number of draws: $\text{SD of average} = \frac{20}{\sqrt{400}} = \frac{20}{20} Show moreā¦
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