A coin is tossed 400 times. use the normal curve approximation to find the probability of obtaining (a) between 185 and 210 heads inclusive; (b) exactly 205 heads; (c) fewer than 176 or more than 227 heads

Answer:0.7925,0.0352,0.0134Step-by-step explanation:Given that a coin is tossed 400 times.Assuming coin to be fair we have p = 0.5E(x) = np = [tex]400(0.5) = 200[/tex]Var(X) = npq = [tex]200(0.5)=100[/tex]Std dev (x) = square root of variance = 10So we can say that binomial approximated to normal after checking conditions X is N(200,10)Since we change from discrete to continuous distribution, continuity correction has to be made.probability of obtaining a) between 185 and 210 heads inclusive; =[tex]P(184.5<x<210.5)\\= P(-1.55<z<1.05)\\=0.4394+0.3531\\=0.7925[/tex](b) exactly 205 heads; = [tex]P(204.5<x<205.5)\\= P(0.45<z<0.55)\\= 0.2088-0.1736\\=0.0352[/tex](c) fewer than 176 or more than 227 heads[tex]P(X<176.5+P(X>226.5)\\\\=P(Z<-2.35)+P(Z>2.65)\\= 0.0094+0.0040\\=0.0134[/tex]