Question

How are the outcomes of flipping a coin 100 times related to the normal distribution?

Answer 1

Solution:

When we flip coin , then

probability of success of head is 0.5 and probability of success of tail is 0.5

Let us flip a coin 100 times.

n = 100 .. (number of trials)

Let X denotes the number of heads occured.

Let p be the success probability of X

So, p = 0.5

X follows Binomial(100 , 0.5)

n * p = 100 * 0.5 = 50

n * (1 - p) = 100 * (1 - 0.5 ) = 0.5

Both are greater than 10 , so we can use normal approximation to the binomial.

So , X follows the normal distribution with

Mean = = n * p  = 50

Standard deviation = =n*p*(1-p) = [100 * 0.5 * 0.5] = 25 = 5

X follows the normal distribution with = 50 and = 5.

Same for number of tails.