Suppose I flip a fair coin one million times.
What's the lower bound that Chebyshev's Inequality provides for estimating
?(498,500≤??≤501,500)?
What's the approximate probability of the above event using the Normal Approximation?
ANSWER::
here mean of distribution=μ=np=1000000*0.5 = | 500000.00 |
and standard deviation σ=sqrt(np(1-p))= | 500.00 |
for normal distribution z score =(X-μ)/σx |
probability =P(498500<X<501500)=P((498500-500000)/500)<Z<(501500-500000)/500)=P(-3<Z<3)=0.9987-0.0013=0.9974 |
(Note:
if using ti-84 use command :normalcdf(498500,501500,500000,500) |
if using excel use command :norm.dist(501500,500000,500,true)-norm.dist(498500,500000,500,true) |
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