9 Question 8. Approximately $10.3 \%$ of American High School students drop out of school before graduation. Choose 10 students entering high school at random, find the probability that no more than 2 drop out?

Step 1 ：This problem can be solved using the binomial distribution model because we have a fixed number of trials (10 students), each trial is independent (one student dropping out does not affect another), and there are only two outcomes (a student either drops out or doesn't).

Step 2 ：The probability mass function of a binomial distribution is given by: \[P(X=k) = C(n, k) * (p^k) * ((1-p)^(n-k))\] where: \[P(X=k)\] is the probability of k successes in n trials, \[C(n, k)\] is the combination of n items taken k at a time, also known as 'n choose k', p is the probability of success on a single trial, n is the number of trials, and k is the number of successes.

Step 3 ：In this case, we want to find the probability that no more than 2 students drop out, which means we need to find \[P(X=0)\], \[P(X=1)\], and \[P(X=2)\], and then add these probabilities together.

Step 4 ：Let n = 10 and p = 0.103. The probability that no student drops out is approximately 0.337, the probability that one student drops out is approximately 0.387, and the probability that two students drop out is approximately 0.200.

Step 5 ：Adding these probabilities together, we get a total probability of approximately 0.925.

Step 6 ：Final Answer: The probability that no more than 2 students drop out is approximately \(\boxed{0.925}\).