OCR MEI S1 — Question 1 5 marks

Exam BoardOCR MEI
ModuleS1 (Statistics 1)
Marks5
PaperDownload PDF ↗
TopicBinomial Distribution
TypeSingle batch expected count
DifficultyModerate -0.8 This is a straightforward application of the binomial distribution formula for part (i), followed by a simple expected value calculation (multiplying probability by 100) for part (ii). Both parts require only direct recall of standard formulas with no problem-solving or conceptual challenges.
Spec2.04b Binomial distribution: as model B(n,p)2.04c Calculate binomial probabilities

1 In a multiple-choice test there are 30 questions. For each question, there is a \(60 \%\) chance that a randomly selected student answers correctly, independently of all other questions.
  1. Find the probability that a randomly selected student gets a total of exactly 20 questions correct.
  2. If 100 randomly selected students take the test, find the expected number of students who get exactly 20 questions correct.

1 In a multiple-choice test there are 30 questions. For each question, there is a $60 \%$ chance that a randomly selected student answers correctly, independently of all other questions.\\
(i) Find the probability that a randomly selected student gets a total of exactly 20 questions correct.\\
(ii) If 100 randomly selected students take the test, find the expected number of students who get exactly 20 questions correct.

\hfill \mbox{\textit{OCR MEI S1  Q1 [5]}}