4.8 Binomial distributionIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 4.8 Binomial distribution

1. A multiple-choice quiz has 12 questions, each with four options of which exactly one is correct. A student guesses every answer at random. Let $X$ be the number of questions answered correctly.
   Use your GDC to find the probability that the student answers exactly 3 questions correctly.2 marks
2. A basketball player scores a free throw with probability 0.7, independently each time. She takes 8 free throws. Let $Y$ be the number of free throws she scores.
   Find the mean and the variance of $Y$.2 marks
3. A factory makes light bulbs. Each bulb is defective with probability 0.04, independently of the others. A box contains 25 bulbs. Let $D$ be the number of defective bulbs in a box.
   (i) Write down the distribution of $D$. (ii) State two conditions that must hold for this model to be appropriate.3 marks