Acoin 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

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 =

Var(X) = npq =

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;

=

(b) exactly 205 heads;

=

(c) fewer than 176 or more than 227 heads

18

step-by-step explanation:

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a² + b²= c²

24² + 7² = c²

c= 25