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When you have to repeatedly take the same test, with constant probability of succeeding/failing, you have to use Bernoulli's distribution. It states that, if you take tests with "succeeding" probability
, and you want to "succeed" k of those n times, the probability is
In your case, you have n=18 (the number of tests), and p=0.3 (the probability of succeeding). We want to succeed between 8 and 12 times, which means choosing k=8,9,10,11, or 12. For example, the probability of succeeding 8 times is
you can plug the different values of k to get the probabilities of succeeding 9, 10, 11 and 12 times, and your final answer will be
Answer: ( X- k )(3x2 - 4x + 7) + 1
Step-by-step explanation: Please find the attached files for the solution
