Question

Let H be the number of heads in 400 tosses of a fair coin. Find normal approximations to:

a) P(190 < H < 210)

b) P(210 < H < 220)

c) P(H = 200)

d) P(H=210)

Answer #1

a)

here mean of distribution=μ=np= | 200 | |||

and standard deviation σ=sqrt(np(1-p))= | 10.0000 | |||

for normal distribution z score =(X-μ)/σx | ||||

therefore from normal approximation of binomial distribution and continuity correction: |

probability = | P(190.5<X<209.5) | = | P(-0.95<Z<0.95)= | 0.8289-0.1711= | 0.6578 |

b)

probability = | P(210.5<X<219.5) | = | P(1.05<Z<1.95)= | 0.9744-0.8531= | 0.1213 |

c)

probability = | P(199.5<X<200.5) | = | P(-0.05<Z<0.05)= | 0.5199-0.4801= | 0.0398 |

d)

probability = | P(209.5<X<210.5) | = | P(0.95<Z<1.05)= | 0.8531-0.8289= | 0.0242 |

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