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4.8 Binomial distributionIB Maths: Applications and Interpretation HL: Flashcards

What these 14 flashcards ask

  • What do n and p stand for in B(n,p)?
  • Give two conditions for a binomial model.
  • Mean of X\simB(n,p)?
  • Variance of X\simB(n,p)?
  • Formula for P(X=x) in a binomial distribution?
  • Write P(X\geq5) using cdf.
  • Write P(2\leq X\leq6) using cdf.
  • Write P(X<4) using cdf.
  • Which GDC function gives P(X=x)?
  • Which GDC function gives P(X\leq x)?
  • Link between binomial mean and SL 4.5?
  • X\simB(8,0.7): mean and variance?
  • Why is drawing from a small group without replacement not binomial?
  • How do you find the smallest k with P(X\leq k)0.9?

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 XX 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 YY be the number of free throws she scores.
    Find the mean and the variance of YY.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 DD be the number of defective bulbs in a box.
    (i) Write down the distribution of DD. (ii) State two conditions that must hold for this model to be appropriate.3 marks
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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).