Question

13) Approximate the probability that in 300 tosses of a fair die, we will obtain exactly 48 fives. a) Without completing any calculations, name all three methods of potentially solving this problem.

TIP: FAIR SIDED DICE 1,2,3,4,5,6

b) Based on the specifics (numerical data) of the problem, evaluate all three methods of potentially solving this problem. Be sure to note which methods can and cannot be used to solve this problem explaining why or why not.

c) Choose the best method to solve this problem. Calculate or approximate the probability based on your decision

Answer 1

a.

We use following methods to solve this problem:

1. By using Binomial distribution

2. By using Poisson approximation to Binomial distribution.

3. By using Normal approximation to Binomial distribution.

b.

Let X= No. of times we get 5

n = 300 and p = 1/6

Since number of trials (300) are very large and number of success is greater than 5, we use Normal distribution to solve this problem.

Note that if number of trials are very large and number of success np < 5 , nq < 5 ,  then we use Poisson approximation.

c.

Normal distribution has parameter = np = 300 * (1/6) = 50 and

Hence required probability, by using continuity correction