Question

8. A fair coin is tossed 60 times. Find the probability that the head appears between 22 and 40 times by using

a. binomial distribution,

b. approximation of Binomial distribution by normal distribution. Discuss why b. is better in practice.

Answer 1

a. Given that,

sample size, n = 60

probability of success, p = 0.5 (for a toss of fair coin)

therefore, probability of failure, q = (1 - p ) = 0.5

number of desired successes, x = between 22 and 40

Thus the probability to be obtained is,

this probability can be obtained using Excel function BINOMDIST(x, n, p, cumulative ) as below:

                      

                      

                      

b. Using Normal approximation to Binomial,

for continuity correction, the range will be 22.5 to 39.5.

mean = np = (60 x 0.5) = 30

standard deviation

therefore,

this probability can be obtained using Excel function NORMSDIST(z) as below: