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Unformatted text preview: ox? _______60____ c) The draws are made …. Circle one: i) with replacement ii) without replacement 4. Fill in the first blank with the number of draws, the second with either “with” or “without” and the third with the letter corresponding to the appropriate box model. Choose from the box models below. Use each box model exactly once. Box A Box B Box C Box D 1 2 3 4 5 6 0 1
1 1 0 0 0 1 1 0 a) A die is rolled 3 times and the sum of the spots is counted. This corresponds to drawing ____3_____times __with________ replacement from Box ___A_ b) A die is rolled 20 times and the total number of 4’s and 5’s are counted. This corresponds to drawing ____20_____times ___with_______replacement from Box ___D___ c) A die is rolled 10 times and you win $1 if you roll an even number but lose $1 if you roll an odd number. This corresponds to drawing ____10_____times ____with______ replacement from Box ___C_ d) A coin is tossed 100 times and the number of heads is counted. This corresponds to drawing ___100______times __with________ replacement from Box ___B_ Chapter 13
The EV and SE of the Sum • Expected Value of the sum of n draws, made at random with replacement from a box: EVsum = n × ave of the box • Standard Error of the sum of n draws, made at random with replacement from a box: €
SEsum = n × SD of the box This is called the Square Root Law • Short –Cut Formula for computing the SD of a box with ONLY tickets marked “a” €€
and “b”: SD= ab  (fraction of "a" tickets )(fraction of "b" tickets) Page 2 € € Study Guide KEY for Exam 3 Practice Problems: 1. 100 draws are made at random with replacement from the box containing 7 tickets:
6
4
2 0 2 4 6 The SD of the box is 4. a) The smallest the sum of the 100 draws could possibly be is __
600______and the largest the sum could be is___600______ b) The Expected Value for the sum of the 100 draws is _____0________ EVsum = n x average of box = 100 x 0 c) The Standard Error of the sum of the 100 draws is____40_____ SEsum = n x SD of box = 100 x 4 = 40 2)
A gambler plays roulette 100 times betting $1 on the numbers 1, 2 and 3 each time. I...
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 Spring '08
 Kim
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