1. A die is rolled one thousand times. The percentages of aces should be around
ID: 3370244 • Letter: 1
Question
1. A die is rolled one thousand times. The percentages of aces should be around _________, give or take ___________ or so.
(a) The first step in solving this problem is i. Computing the SD of the box. ii. Computing the average of the box. iii. Setting up the box model. Choose one option and explain.
(b) Now solve the problem.
(c) Find the chance that the percentage of aces in the one thousand rolls is 19 or more.
(d) For more rolls, would the give or take to up or down? Explain.
(e) Find the number of rolls necessary for the give or take to be 2.5%.
Explanation / Answer
Solution:
The average of the box is 1/6 and the SD is 1 / 6 * 5 / 6 ? 0.373.
The expected value is 1000 * 1/6 ? 166.7.
The SE is 1000 *0.373 ? 11.8.
The number of aces will be around 167, give or take 12 or so.The SE for the percentage is 12 out of 1000, which is 1.2%.
The percentage of aces should be around 16.67 %, give or take 1.2% or so.
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