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complement-clt

# complement-clt - Stat 100A/Sanchez Winter 2013 Examples of...

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Stat 100A/Sanchez Winter 2013. Examples of applications of the CLT. Done in lecture. Please, watch video for full lecture. Student scores on exams given by a certain instructor have mean 74 and standard deviation 14. This instructor is about to give two exams, on to a class of size 25 and the other to a class of size 64. (a) Approximate the probability that the average test score in the class of size 25 exceeds 80. (b) Repeat part (a) for the class of size 64. (c) Approximate the probability that the average test score in the larger class exceeds that of the other class by over 2.2 points. (d) Approximate the probability that the average test score in the smaller class exceeds that of the other class by over 2.2 points. 25 . ) 3 . 3 0 2 . 2 ( ) 2 . 2 ( ) ( 25 . ) 3 . 3 0 2 . 2 ( ) 2 . 2 ( ) 25 14 64 14 , 0 ( ~ ) ( 0003 . ) 8 / 14 74 80 ( ) 80 ( ) ( 016 . ) 5 / 14 74 80 ( ) 80 ( ) ( ) / 14 , 74 ( ~ 2 2 25 64 = < = < = > = > + = = > = > = > = > Z P Y P d Z P Y P N X X Y c Z P X P b Z P X P a n N X 2. A ski lift is designed with a total load limit of 10,000 pounds. It claims a capacity of 50 persons. An expert in ski lifts thinks that the weights of all the people using the lift have a

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