Problem 3. (15 points) Ada Nixon, a student, has just begun a 24-question, multiple-choice exam. For...

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Problem 3. (15 points) Ada Nixon, a student, has just begun a 24-question, multiple-choice exam. For each question, there is exactly one correct answer out of four possible choices. Unfortunately, Ada hasn't prepared well for this exam and has decided to randomly select an answer choice for each question. (a) (1 point) For a given question, what is the probability Ada picks the correct answer, assuming each answer choice is equally likely to be selected? Answers can be left as fractions. Otherwise, round your final answer to two decimal places. (b) Assume X = the number of questions Ada answers correctly is binomially distributed. %3D i. (2 points) Write down the notation with parameters for the distribution of X. ii. (2 points) What is the mean of the number of questions Ada will answer correctly? Show your work. Round your final answer to the next whole number. iii. (2 points) What is the variance of the number of questions Ada will answer correctly? Show your work. Answers can be left as fractions. Otherwise, round your final answer to one decimal place if necessary. iv. (3 points) If Ada answers at least 13 questions correctly, she will receive a passing grade. What is the probability that Ada receives a passing grade? Show your work. Answers can be left as fractions. Otherwise, round your final answer to three decimal places if necessary. (c) (5 points) Suppose Ada comes across a question for which she knows two of the answer choices are certainly wrong, which means the correct answer must be one of the two remaining choices. Assuming Ada will answer every other question using the same random selection procedure as before, will the number of questions she answers correctly remain binomially distributed? State Yes or No and explain why. Problem 3. (15 points) Ada Nixon, a student, has just begun a 24-question, multiple-choice exam. For each question, there is exactly one correct answer out of four possible choices. Unfortunately, Ada hasn't prepared well for this exam and has decided to randomly select an answer choice for each question. (a) (1 point) For a given question, what is the probability Ada picks the correct answer, assuming each answer choice is equally likely to be selected? Answers can be left as fractions. Otherwise, round your final answer to two decimal places. (b) Assume X = the number of questions Ada answers correctly is binomially distributed. %3D i. (2 points) Write down the notation with parameters for the distribution of X. ii. (2 points) What is the mean of the number of questions Ada will answer correctly? Show your work. Round your final answer to the next whole number. iii. (2 points) What is the variance of the number of questions Ada will answer correctly? Show your work. Answers can be left as fractions. Otherwise, round your final answer to one decimal place if necessary. iv. (3 points) If Ada answers at least 13 questions correctly, she will receive a passing grade. What is the probability that Ada receives a passing grade? Show your work. Answers can be left as fractions. Otherwise, round your final answer to three decimal places if necessary. (c) (5 points) Suppose Ada comes across a question for which she knows two of the answer choices are certainly wrong, which means the correct answer must be one of the two remaining choices. Assuming Ada will answer every other question using the same random selection procedure as before, will the number of questions she answers correctly remain binomially distributed? State Yes or No and explain why.

Answer rating: 100% (QA)

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