Normal approximation to the binomial and Poisson

Normal approximation to the binomial and Poisson Quiz

Spec 3.2 · Edexcel International A Level Further Maths: Quiz

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  1. 1. A normal approximation is used for X∼B(100,0.5)X\sim\mathrm{B}(100,0.5). What is the variance of the approximating distribution?

    • A. 5050
    • B. 2525
    • C. 55
    • D. 25002500

  2. 2. X∼Po(16)X\sim\mathrm{Po}(16) is approximated by a normal YY. Which expression approximates P(X>20)\mathrm{P}(X>20)?

    • A. P(Y>19.5)\mathrm{P}(Y>19.5)
    • B. P(Y>20)\mathrm{P}(Y>20)
    • C. P(Y>20.5)\mathrm{P}(Y>20.5)
    • D. P(Y>21)\mathrm{P}(Y>21)

  3. 3. X∼B(50,0.5)X\sim\mathrm{B}(50,0.5). Using a normal approximation with a continuity correction, P(X≥28)=P(Z>a)\mathrm{P}(X\ge28)=\mathrm{P}(Z>a). Find aa to 3 d.p.

    • A. 0.7070.707
    • B. 0.8490.849
    • C. 0.9900.990
    • D. 0.5660.566

  4. 4. Which binomial distribution is best approximated by a normal distribution?

    • A. B(10,0.5)\mathrm{B}(10,0.5)
    • B. B(200,0.01)\mathrm{B}(200,0.01)
    • C. B(20,0.95)\mathrm{B}(20,0.95)
    • D. B(200,0.48)\mathrm{B}(200,0.48)

  5. 5. X∼Po(30)X\sim\mathrm{Po}(30). Using a normal approximation with a continuity correction, find P(X≤25)\mathrm{P}(X\le25).

    • A. 0.1810.181
    • B. 0.2060.206
    • C. 0.1580.158
    • D. 0.2610.261

Quiz