Question

13. We created a test to determine if a coin is fair. For this test we used the .95 to .05 split criteria. A portion of the Binomial Distribution, with 150 trials and 3 values of p, is given. Clearly our "OK to Bet" Region is [0, 85] and our "Cheater" Region is [86, 150]. Determine the probability of catching a cheater that is using a p 6 cheater coirn Answer 81 0.85577 0.07898 0.00003 82 0.88973 0.10613 0.00005 83 0.91755 0.13951 0.00010 84 093974 0.17944 0.00020 85 0.95696 0.22594 0.00037 86 0.96999 0.27867 0.00068 87 0.97957 0.33685 0.00120 88 0.98642 0.39933 0.00207 89 0.99120 0.46461 0.00349

Answer 1

The Binomial PMF is .

P(X=x)=(C)px (1-p)n-x , x =0, 1,2, , n

Here .

n- 150,p 0.6

The probability of the Cheater region is

P (X > 86) = 1-P(X < 86) P (X > 86) = 1-Σ (rso) 0.6"(1-0.6)150-х P(X 86) = 0.7741

The R command is

> 1-pbinom(85,150,0.6)
[1] 0.7740556