Statistics Homework Solutions 105

Statistics Homework Solutions 105 - 105 SECTION 4.11 X Y...

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SECTION 4.11 105 The number of particles emitted by both masses together is S X Y . Since X and Y are independent, and both approximately normal, S is approximately normal as well, with mean μ S 100 125 225 and standard deviation σ S 100 125 15. The z -score of 200 is 200 225 15 1 67. The area to the left of z 1 67 is 0.0475. P S 200 0 0475. (b) Let X be the number of particles emitted by mass A and let Y be the number of particles emitted by mass B in a two-minute time period. Then X Poisson 40 and Y Poisson 50 . Now X is approximately normal with mean 40 and variance 40, and Y is approximately normal with mean 50 and variance 50. The difference between the numbers of particles emitted by the two masses is D Y X . Mass B emits more particles than mass A if D 0. Since X and Y are independent, and both approximately normal, D is approximately normal as well, with mean μ D 50 40 10 and standard deviation σ D 50 40 9 486833. The z -score of 0 is 0 10 9 486833 1 05. The area to the right of z 1 05 is 1 0 1469 0 8531.
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