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Statistics Homework Solutions 104

# Statistics Homework Solutions 104 - 104 Let n be the...

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104 CHAPTER 4 9. Let n be the required number of measurements. Let X be the average of the n measurements. Then the true value is μ X , and the standard deviation is σ X 1 n . Now P μ X 0 25 X μ X 0 25 0 95. In any normal population, 95% of the population is within 1.96 standard deviations of the mean. Therefore 1 96 σ X 0 25. Since σ X 1 n , n 61 47. The smallest value of n is therefore n 62. 11. (a) Let X represent the number of defective parts in a shipment. Then X Bin 400 0 20 , so X is approximately normal with mean μ X 400 0 20 80 and standard deviation σ X 400 0 2 0 8 8. To find P X 90 , use the continuity correction and find the z -score of 90.5. The z -score of 90.5 is 90 5 80 8 1 31. The area to the right of z 1 31 is 1 0 9049 0 0951. P X 90 0 0951. (b) Let Y represent the number of shipments out of 500 that are returned. From part (a) the probability that a shipment is returned is 0.0951, so Y Bin 500 0 0951 . It follows that Y is approximately normal with mean μ Y 500 0 0951 47 55 and standard deviation σ Y 500 0 0951 0 9049 6 5596. To find P Y 60 , use the continuity correction and find the z -score of 59.5. The z -score of 59.5 is 59 5 47 55 6 5596 1 82. The area to the right of
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