Question

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?

**Please be very descriptive in answer and write neatly!! :)

Answer 1

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)