Final answer:
To find the probability that the number of correct answers on the SAT test will be greater than 4, we can use the binomial distribution formula. We can use technology such as the TI-83, 83+, 84, 84+ calculator to easily find the cumulative probability P(X > 4) by subtracting the cumulative probability P(X ≤ 4) from 1.
Step-by-step explanation:
To find the probability that the number of correct answers on the SAT test will be greater than 4, we can use the binomial distribution formula. The probability of getting exactly k correct answers out of n questions is given by the formula P(X = k) = C(n, k) * p^k * (1-p)^(n-k), where n is the number of questions, k is the number of correct answers, and p is the probability of success (being correct) for each question.
In this case, n = 15, p = 0.65, and we want to find the probability that the number of correct answers will be greater than 4. We can calculate this by finding the sum of probabilities for k = 5 to 15 using the formula.
To calculate this manually, it would be quite tedious. However, we can use technology such as the TI-83, 83+, 84, 84+ calculator to easily find the cumulative probability P(X > 4) by subtracting the cumulative probability P(X ≤ 4) from 1. The rounded result is the probability that the number of correct answers will be greater than 4.