Question

A set of 1100 exam scores is normally distributed with a mean = 84 and standard deviation = 4. Use the Empirical Rule to complete the statements below. How many students scored higher than 84? How many students scored between 80 and 88? How many students scored between 76 and 92? How many students scored between 84 and 88? How many students scored lower than 80? How many students scored lower than 88?

Answer 1

Solution Let X: Set of too exam scosces Here XN Normal (84, 42) Normal ( Bell shaped) cowe using empinical rule is as follows: 34% 1341 0.15* 21351 0.151. 13.5.111.21357 (13.5 21-20 allo 04428 se1736 o = 4 Here a = 84 elco: 84-4 =80 elts 844¢= ss i-20 = 84-264)= 76 41725 = 84 +264)= 92 ei-30 = 84-3(4) = 72 Let 30 = 94 +364) = 96 Here No 1100 1) How many students scored higher thaso. 84 Nantes Saadets Number of students scored higher than $$ NAPCx384) to We have uto=84 from above empirica.come the free to the right of is 34%. + 3:57. +3.357.0.15). S01 p( x > 84 )= o.so Nap(x384) looto.so SSO Therefore sso stecents scored higher than 84.

How many students scored between 80 sand & Pie N* go<x<88 We have" Il-o: 80, from above propiscal carve the area between lo and 34% + 347, 68.1. P ( 80 < x < 88 =0.68 ، کر ک_يد Nix PC Box XC88)= 1 100x 0.68 748 Therefore 748 stuchents scored between so and Hoe scany students scored scored between 76 and 927 ie. Nx 13(76Lcga) We have, el-25= 76, e+20= 92 from above capirical cone the grea between ei-2s and utzo is 13.5%. +344. 434% +13:51 gsu P( 76 < x < g2) ongs Nx P( 762 X 292) = 1100xo.g5 1045 Therefore 1045 students scored between 76 and 92

How mocny students Scored between 84 and 88. Pie NPC regexs 88) lwe haves M = 84 بل from above enpinsal care the area between and eto is 34% i. pl. 84 <x< 88:') = 0,34 Nxip(845 X 488)= 1100x0.34 374 Therefore 374 students scored between 84 How many students scored lower than 80? ie. Nape x < 80) have; e- 8.0 from above empirical core the cree to the left off eines is 13.5%+2.35% 40:151, 16°1 ². P(x280) = 0.16 wx PCX<80): 1100*0.16 176 Therefore 176 students scored lower than so

6) scored lower than 88 ? Hawa sing students pie. Nx PCXS 88) He have Mto=88 from above empirical cone the area to the left of into is 0 15 % + 2.35% 13.5% +34!. +34). 84%. ( x 88 ) = 08 + NX PC 8.5 88) = 1100*0.84 924 Therefore 924 students scored lower than 88.