Question

2. A normal distribution of Boer goat weights at age 6 months defined with u = 30 kg and = 3 kg. Determine theoretical proportions of goats: a) more than 35 kg; b) less than 35 kg; c) less than 33 and more than 25 kg; d) What is the theoretical lowest value for an animal to be included among the heaviest 20%; e) What is the theoretical mean of animals with weights greater than 35 kg

Answer 1

let goe weights denoted by variable x , ginen that Xm N(30,3%) 1 XNlWire) la) P(x>35) After Normalizing p(x>35) = P(x=> 35730 ) = p<z>1.67) from Normal Table Plz>1067)= 0.0474 (b (x235) = P(Z<5%) = P( 2<1.67) = 0,9525 o p(25<x<33) = P(-25-30 < x < 33-30 = P61672 z<1) = P(1.676220) + POCZ<0). Ś0.4525 + 0.3413 30.7938 @ Among haviest 20% implies upper 20% or lower dog P(x2x) = 0.20 PC XSA > *3) = 0.2 Plz > 45,3°) 30.20 from table Pl 27.0.84 0.20 30 =0,84 -) 1'=30+3x0,84 = 32.52 = 32.521