Question

we toss a fair coin 100 times. What is the probability of getting more than 30 heads?

Answer 1

GIVEN:

A fair coin is tossed 100 times.

TO FIND:

The probability of getting more than 30 heads

SOLUTION:

Given that number of trials (coin flips)

Let X be the number of heads which follows binomial distribution with equal probability of success (getting head) and probability of failure (getting tail) .

Using Central limit theorem,

If is sufficiently large, then it is appropriate to use the normal approximation to the binomial.

The general rule of thumb is that is sufficiently large if:

and

and

The two conditions are satisfied which implies n is large. Thus the binomial is approximated to normal distribution with mean and standard deviation .

To calculate the probability we convert the raw score (X) into standard score (Z) using the formula given by,

where

and

  

  

  

The probability of getting more than 30 heads is

{Since }

  

  

  

Using the z table, the probability value is the value with corresponding row -4.0 and column 0.00.

  

  

The probability of getting more than 30 heads is .