Final answer:
To calculate the probability that the number of correct answers is fewer than 4 on a 6-question multiple choice test with each question having a probability of correct answer p=0.35, use the binomial probability distribution either by calculating individual probabilities for 0, 1, 2, and 3 correct answers and adding them together, or using the cumulative binomial probability function on a calculator.
Step-by-step explanation:
To find the probability that the number of correct answers is fewer than 4 (P(X<4)) when making random guesses on a six-question SAT test where the probability of getting a question right is 0.35, we can use the binomial probability formula or a calculator with binomial distribution functions.
Use the formula P(X = x) = (nCx) * (p^x) * ((1 - p)^(n-x)), where:
- n is the number of trials (6 in this case),
- p is the probability of success on a single trial (0.35), and
- x represents the number of successful trials.
Calculate the probabilities for x being 0, 1, 2, and 3 and add them up.
Alternatively, use a calculator function like binomcdf for cumulative probabilities: P(X < 4) = binomcdf(6, 0.35, 3).