(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 the other of size 25, and is about to give an exam to both classes mean 70 and standard deviation 12 The instructor is teaching two classes, one of size 81 and (a) Approximate the probability that the average test score in the class of size 81 exceeds 75 Probabiaty s (b) Repeat part (a) for the class of size 25 Probability (c) Approximate the probability that the average test score in the larger class exceeds that of the other by more than 1 6 points Probablity (d) Approximate the probatbility that the average test score in the smaller class exceeds that in the other by more than 1 6 ponts Probabiity

Explanation / Answer

a) for class of 81 ; std error =std deviation/(n)1/2 =12/(81)1/2 =1.3333

hence probability =P(X>75)=P(Z>(75-70)/1.3333)=P(Z>3.75)=0.0001

b)

for class of 25 ; std error =std deviation/(n)1/2 =12/(25)1/2 =2.4

hence probability =P(X>75)=P(Z>(75-70)/2.4)=P(Z>2.0833)=0.0186

c)

std error between two classes =(122/81+122/25)1/2 =2.7455

therefore P(X>1.6)=P(Z>(1.6-0)/2.7455)=P(Z>0.5828)=0.2800

d) similarly here P(X<1.6)=P(Z<-0.5288)=0.2800

please revert

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