Question #7 Es esc 5 6 7 2 304 THE EXPECTED VALUE AND STANDARD ERROR [CH. 171 6,
ID: 3329414 • Letter: Q
Question
Question #7
Es esc 5 6 7 2 304 THE EXPECTED VALUE AND STANDARD ERROR [CH. 171 6, (a) A coin is tossed 10,000 times. What is the chance that the n will be in the range 4,850 to 5,150? (b) A coin is tossed 1,000,000 times. What is the chance that the number of heads will be in the range 498,500 to 501,500? 7. Fifty draws are made at random with replacement from the box D0 there are 33 among the draws. The expected number of L 'sis observed number is , the chance error is the , and the SE is 8. A computer program is written to do the following job. There is a box with ter blank tickets. You tell the program what numbers to write on the tickets, and how many draws to make. Then, the computer will draw that many tickets at random with replacement from the box, add them up, and print out the sum-but not the draws. This program does not know anything about coin tossing. Still, you can use it to simulate the number of heads in 1,000 tosses of a coin. How? 9. A die is rolled 100 times. Someone figures the expected number of aces a 100 x 1/6-16.67, and the SE as ~/100 x ~/1/6x5/68 3.73. (An ace sb this right? Answer yes or no, and explain. The answers to these exercises are on p. A75. REVIEW EXERCISES One hundred drate uiExplanation / Answer
Q.6 (a) Number of coins = 10,000
Expected number of heads = 10000 * 0.5 = 5000
standard deviation of number of heads = sqrt (10000 * 0.5 * 0.5) = 50
Pr(4850 < X < 5150 ; 5000 ; 50) by normal distribution
so Z2 = (4850 - 5000)/ 50 = -3
Z1 = (5150 - 5000)/ 50 = 3
so Pr ( +- 3) = (3) - (-3)
where is the normal standard cumulative distribution.
Pr ( +- 3) = 0.9987 - 0.0013 = 0.9974
(b)
Number of coins = 10,00,000
Expected number of heads = 1000000 * 0.5 = 500000
standard deviation of number of heads = sqrt (1000000 * 0.5 * 0.5) = 500
Pr(4850 < X < 5150 ; 500000 ; 500) by normal distribution
so Z2 = (498500 - 500000)/ 500 = -3
Z1 = (501500 - 500000)/ 500 = 3
so Pr ( +- 3) = (3) - (-3)
where is the normal standard cumulative distribution.
Pr ( +- 3) = 0.9987 - 0.0013 = 0.9974