Question

A certain standardized test's math scores have a bell-shaped distribution with a mean of 530 and a standard deviation of 110. Complete parts (a) through (c). (a) What percentage of standardized test scores is between 200 and 860? % (Round to one decimal place as needed.) (b) What percentage of standardized test scores is less than 200 or greater than 860? % (Round to one decimal place as needed.) (c) What percentage of standardized test scores is greater than 750? % (Round to one decimal place as needed.)

Answer 1

Let & be the certain standardized test's math score. given that, XNN(4= 530, 6²= (1107²) tras a te mean, et = 350, S., 6 = 110. @ Here we have to find percentage of standardized test score is between 200 and 860. je PC 200 < x 3800) know that, if ANN(416²) then a = x-el (1) we "P( 200 < x <800] = P( 200-530 X-530 860-530 < 110 10 110 = P(-3<2<3) = Plz(3) - P(Z <-3) P(223) P(Z 73) (.: standard normal dista is symmetric :1-P (273) - PC273) = 1-2 P(273) = 1-2 X 0.0013499 0.9973 P(200< x 800 je. P1200 ( XC860) = 99.7 l. i. Ans 99.71. ③ we have to find percentage of standardized test score is less than 200 of greater than 850 - PC XL200) SUP ( X >860) PCX< 200) + P(x?960) P/X-530 200-530 110 PLATNO X-530> 860-530 1930) + P (*100 = P(Z <-3) + P(273) 110 PLZ73) + Plz73)

PLX (200) + P(X7860) = 2 PC 2273) 22x0.0013499 = 0.00 26998, standardized test score .. Required percentage of is 0.3% © Here, we have to find percentage of standardized test score is greater than 750. i.e PC X7750 ) - PC pl X-530 > 750-530 110 110 - P(272) Ñ 0.023 " P(X7750) = 0.02275 ie PCX2750) = 2.3 % ". Ansi 203%