Question

According to FIFA, the average height of professional goal keepers is 71 inches, with a standard deviation of 1.25 inches, and is normally distributed. Use this information to address the following:

a. What is the probability a goal keeper is shorter than 70 inches?

b. What is the probability a goal keeps is taller than 74 inches?

c. What is the probability a goal keeper is between 69 and 73 inches?

d. What goalie height is associated with the 75th percentile?

e. What goalie height is associated with the 50th percentile?

Answer 1

::. According to FFA mean heign- of professional goal keeper 1 inches, Standard deviation 1.25 inches (ој Рnob Газоан. keep en hoo - Skoлғ than to inches]. : pr x < 70] prxc4179-7177 : 7:25 1125 =P[<<+08] T where I ONCO,1). - 10.212] (6) Prob[ a goal keeper is taller than 44 ünches ] = PTXy447 pix-Ly 44 - 7 . :P[ty =P[Z) 919 I where Z N (0,1)] = 10:0081 - le probt a goal Keeper is between 69 and 73 inches. I apt: 69% *73]: [ 69. RMC73-77 P[-46.87146]

s [<16] - P[z<-N6] = 0.94.55 -0.055 = 10:89 , 5. d) 75 the percentile of standard Normal distribution means that the lower probability will: 68 0.75 Now, P[xx 60:45] = 0.45 * PTX-71 20.75 -4! 30:45 17:25 7:25 Y PI Z 2 2075 -71 7 = 8.75. 1:25 from the table nee have got that the point will be a cargo - 11 )/11255 0.6743 71:8495 172.1 (e) Similarly nee will calculate the 50% probie 50th percentile prx < Coigo ] = 0.50 -=PL 725 yer x-4 10.50 - 0.50 * PEZT 20.5-7130150 1.2.5. from table will have (cos'-719/1.25 = evento o => You 91.1 - Thanks!! 7:25 -