(1 point) Let us suppose that a certain probability instructor manages, with pro

Question

(1 point) Let us suppose that a certain probability instructor manages, with probability 1, to write exams that have mean 70 and standard deviation 12. The instructor is teaching two classes, one of size 64 and the other of size 36, and is about to give an exam to both classes. (a) Approximate the probability that the average test score in the class of size 64 exceeds 75. Probability (b) Repeat part (a) for the class of size 36. Probability (c) Approximate the probability that the average test score in the larger class exceeds that of the other by more than 2.6 points. Probability (d) Approximate the probability that the average test score in the smaller class exceeds that in the other by more than 2.6 points Probability

Explanation / Answer

a) std error of mean =std deviation/(n)1/2 =12/(64)1/2 =1.5

hence P(X>75)=P(Z>(75-70)/1.5)=P(Z>3.3333)=0.00043

b)

std error of mean =std deviation/(n)1/2 =12/(36)1/2 =2

hence P(X>75)=P(Z>(75-70)/2)=P(Z>2.5)=0.00621

c) for mean difference =0

here std error of difference =(1.52+22)1/2 =2.5

hence P(X>2.6)=1-P(Z<(2.6/2.5))=1-P(Z<1.04)=1-0.85083=0.14917

d) similar as above 0.14917

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