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