Mathematics · AQA 7357 · Topic N

Statistical distributions

The binomial and normal distributions and when each is a sensible model.

  • 3 sub-topics
  • Taught in Year 13
  • 63 practice questions
  • 3 animated lessons
Practice questions (63) Lessons Worksheets All AQA Mathematics topics

What the specification says

Every sub-topic AQA can examine in this topic, with its reference number from the official specification. The Y12 and Y13 tags show when each sub-topic is usually taught.

  1. N1Discrete distributions, including the binomial distributionY13
  2. N2The normal distributionY13
  3. N3Choose an appropriate distributionY13

Try 3 questions

Easy, medium and hard questions from this topic, each with a worked solutions and the mark for every step. All 63 questions in this topic, free, no account needed.

Statistical distributions

Easy

A binomial probability · Year 12 · 2 marks

X∼B(10,0.3)X \sim \mathrm{B}(10, 0.3)
  1. Find P(X=3)\mathrm{P}(X = 3).
    (2)
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  1. Choose which 3 trials succeed, then multiply the probabilities.(103)(0.3)3(0.7)7\dbinom{10}{3}(0.3)^3(0.7)^7
  2. =0.267= 0.267

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Statistical distributions

Medium

Binomial probabilities · Year 12 · 3 marks

X∼B(20,0.3)X \sim \mathrm{B}(20, 0.3)
  1. (a)
    Find P(X≤4)\mathrm{P}(X \le 4).
    (1)
  2. (b)
    Find P(X≥8)\mathrm{P}(X \ge 8).
    (2)
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Part (a)1 mark

  1. Use the cumulative binomial function on your calculator with n=20n = 20, p=0.3p = 0.3.P(X≤4)=0.2375\mathrm{P}(X \le 4) = 0.2375

Part (b)2 marks

  1. The calculator gives 'less than or equal to', so use the complement.P(X≥8)\mathrm{P}(X \ge 8)=1−P(X≤7){}= 1 - \mathrm{P}(X \le 7)
  2. Subtract from 1.=1−0.7723=0.2277= 1 - 0.7723 = 0.2277

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Statistical distributions

Not needed for Year 12Hard

Finding the mean and standard deviation · Year 13 · 6 marks

X∼N(μ,σ2)X \sim \mathrm{N}(\mu, \sigma^2), P(X<40)=0.2\mathrm{P}(X < 40) = 0.2 and P(X>60)=0.1\mathrm{P}(X > 60) = 0.1.
  1. Find μ\mu and σ\sigma.
    (6)
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  1. The zz-value with 0.2 below it is negative.40−μσ=−0.8416\dfrac{40 - \mu}{\sigma} = -0.8416
  2. The zz-value with 0.9 below it.60−μσ=1.2816\dfrac{60 - \mu}{\sigma} = 1.2816
  3. Two simultaneous equations.Subtract: 20=2.1232σ20 = 2.1232\sigma
  4. σ=9.42\sigma = 9.42, μ=47.9\mu = 47.9

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