Answer:
0.7925,0.0352,0.0134
Step-by-step explanation:
Given that a coin is tossed 400 times.
Assuming coin to be fair we have p = 0.5
E(x) = np = [tex]400(0.5) = 200[/tex]
Var(X) = npq = [tex]200(0.5)=100[/tex]
Std dev (x) = square root of variance = 10
So 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]
