Question

In the last 7 years, 500 students who have taken the Mathematics final exam have averaged 55 points and a variance of 225. By applying the normal distribution, the final grade of a selected student a) Find the probability that it is 60 or less. b) Find the probability that it is between 60 and 75. c) What is the grade with the probability of exceeding 3%? d) At 95% confidence level, find the confidence interval limits for the mass mean. e) If the passing grade is 60, interpret grade success and variability of grades.

Answer 1

Answer: Criven data normally dusterssuted with mean (ui= si pornts and raisance cor) - 225 then standard deveation (0) = 1225 Lett be a normal dostrosutoon random cargable - 15 Nuw, 1- (C) The pensability that it A 60 ot less pex's.co)- PC -4.60 x-4, 60-17 P12 0.377971), PL 2 20.37) From the standard holmal table 0. 62970 20. 6297 ip(x268)=0.6293 probability that it is setween 60 and tot P(602X2 75) = P(X(75)-PLX-60) = P(2-4275 - 35 ) - P(x-Y COST 71241.31731) - P(22 0.73713] .P(2.21.33)-P(220.33) From the Handad normal tasle 6) the

© PL GOLXL75) = 0.90824-0.62930 = 0.27894 ~ 0.2789 2 P (60 2XL75) = 0.2789 & the grade with the prosability of excluding IV. m. It can se wrothen as P(x > x) = 3% P(X) 2) = |- P(XLU-0.03 P.(XLX)= 1-0.03 P(XZN)= 0.97% REKO Plus - 15 ) - 0.97 from the Standaid nolmal table, for 0.97 O. 03 prosability t-rallers lisa X-55 = 1.89 ار No 1.89 x 15 X = (1.59X15) +55 = 83.35 .:(X=83.15] thwks nequined geade valere 44 81.95.

3 d the mean de For 95%. Contodence. level 2-value as 1.96 No requand 95% confidence interval is Con remula for confodence internal for CIB M + 2 C and nou CI= MI 2 CM) 154 1.9! (vro 554 1.96 (0.6.706202939) 2 55+ 1.3148079706 = (57.685 1920292, 56.3148079708) ~ [51. 68, 56.32) For 2 decimal places .. CI = (57.68, 56.32) 53.68 < u < 56.32