Question

SORU 1 An exam is given to all senior high school students, the standard deviation for all the students is given as 30. The average score for 50 students on the exam is 540. Assume the means to be measured to any degree of accuracy assume that scores are Gaussian distributed Find the 90s confidence interval (C) for the average score of all students taking the exam, Find the prediction interval for the score of the next student chosen at random tot one of the original 50 students

Answer 1

Let M and respectively denote the population standard mean and deviation scores. of Here we the assume that scores are normally distributed and given o = 30. the Here population distribution is normal and the population standard deviation is known. A 10011-2) 7. C.I. C. I for u is (n-E, X + E), where Za un

ñ = sample mean sample E = of error size n - 0 ma •gin Level da i confidence confidence Given that Level = 0. go, no n=50 540. 2 - I-ogo = 0.10. . Z Zo.10 Zo.o5 ola 2 1.645

E = Zo.o5t SIE 30 - 1 645 X 50 6.98. the The go :) c. I. for of the all score average students taking is exam

(n-E, Ť+E) (540-6.98,540+ 6.98) 533.02, 546.98 78) the In this problem, the population distribution is normal and population standard deviation to is known. The prediction for the next student random 100(1-2)/ interval (P.I.) score of the chosen at is X - Za xo ita 2 a + Za 1 + 2

P. I. for the : The go/ the next score of chosen at student is random 1 + a- Zoo Х .05 Zo.05 x

1s 50 590 - 1.645 x 30x 540 + 1.695 x 30 x 50 - (490.16, 589.84)