Question

Suppose a fair coin is tossed 280 times. Find the probability that the number of Heads observed is 151 or more. Use Binomial Distribution and Normal Approximation and compare the results.

Answer 1

Here x: random variable which is number of head in total 280 tossed coin  i.e n=280, p=q=0.5,

We know that for binomial distribution Mean = np = 280*0.5 = 140    and Variance = npq = 280*0.5*0.5 = 70.

Since Binomial approxite to normal when p=0.5 and n is large so x ~ normal (mean = np, var = npq).

So X be random variable which is number of head in total tossing of coins.

P(x >=151) = P(Z>=(151-140)/sqrt(70)) = 1- P(Z<1.3147) = 1- 0.906=0.094.

So probability of getting 151 head or more in 280 tosses is 0.094