Question

RAPID predicts a student's likelihood of end-of-year grade-level success, on the Reading Comprehension subtest of the 10th edition of the Standford Achievement Test

a True
b false

Answer 1

The probability of passing a 10-question true-false quiz with at least a 70 percent grade by randomly guessing is found by calculating the sum of the probabilities of getting at least 7 questions right using the binomial probability formula.

Step-by-step explanation:

To find the probability of a student passing a 10-question true-false quiz by randomly guessing and getting at least 70 percent correct, we first need to understand what this percentage represents in terms of the number of questions. Since the quiz has 10 questions, getting 70 percent correct means getting at least 7 questions right.

Since the answers are guessed randomly, each question has a 50 percent chance of being answered correctly. We can use the binomial probability formula to calculate the probability of getting k successes (correct answers) in n trials (questions) with the probability p of success on a single trial:

Binomial probability formula: P(X = k) = nCk × (p)^k × (1-p)^(n-k)

We are interested in the sum of the probabilities of getting exactly 7, 8, 9, or 10 correct answers, which involves calculating the probabilities separately and then adding them up. Alternatively, this can be calculated using statistical software or a scientific calculator that has binomial probability functions.