## 1. Find the probability of getting between 40 and 60 heads inclusive in 100 toss

1. Find the probability of getting between 40 and 60 heads inclusive in 100 tosses of a fair coin.2. To test the hypothesis that a coin is fair adopt the following decision rule:Accept the hypothesis if the number of heads in a single sample of 100 tosses is between 40 and 60 inclusive.Reject the hypothesis otherwise.(a) Find the probability of rejecting the hypothesis when it is actually correct.(b) Graph the decision rule and the result of part (a).(c) What conclusions would you draw if the sample of 100 tosses yielded 53 heads? And if it yielded 60 heads?(d) Could you be wrong in your conclusions about part (c)? Explain.3. Using the binomial distribution and not the normal approximation to the binomial distribution design a decision rule to test the hypothesis that a coin is fair if a sample of 64 tosses of the coin is taken and a significance level of 0.05 is used. Use MINITAB to assist with the solution.