Question

Binomial distributions are approximately normal when the number of trials is large, and the probaility of success is not near zero or one. A player flips an unbiased coin 1,296 times.

a. What is the probability of the coin landing on heads between 612 and 684 times?

Answer 1

Here, the unbiased coin is tossed 1296 times.

Now, the probability that the coin lands head, is 0.5.

As the number of tosses is too large, so we can do the normal approximation to binomial.

Here, n = 1296 and p = 0.5.

So, the mean is

n*p

=1296*0.5

=648

And the standard devaition is

=sqrt(n*p*(1-p))

=sqrt(1296*0.5*0.5)

=sqrt(324)

=18

So, if X be the random variable denoting the number of heads in 1296 tosses, then, we can say X follows normal with mean 648, and standard devaition of 18.

Now, we have to find the probability of the coin landing heads between 612 and 684 times.

So,

we have to find

So, the probability of the coin landing heads between 612 and 684 times, is 0.9544.