A coin is tossed 400 times. use the normal curve approximation to find the probability of obtaining (a) between 185 and 210 heads inclusive;

Question

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

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Madelyn 16 hours 2021-10-12T07:54:59+00:00 1 Answer 0

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    2021-10-12T07:56:42+00:00

    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 = 400(0.5) = 200

    Var(X) = npq = 200(0.5)=100

    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;

    =P(184.5<x<210.5)\\= P(-1.55<z<1.05)\\=0.4394+0.3531\\=0.7925

    (b) exactly 205 heads;

    = P(204.5<x<205.5)\\= P(0.45<z<0.55)\\= 0.2088-0.1736\\=0.0352

    (c) fewer than 176 or more than 227 heads

    P(X<176.5+P(X>226.5)\\\\=P(Z<-2.35)+P(Z>2.65)\\= 0.0094+0.0040\\=0.0134

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