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2.4 N: Statistical distributions

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Question 65

The random variable X X\,X has the distribution X∼B(n,0.25)X \sim B(n, 0.25)X∼B(n,0.25), and

P(X=0)<0.01P(X = 0) < 0.01P(X=0)<0.01

a.

Show that n>log⁡0.01log⁡0.75\displaystyle n > \frac{\log 0.01}{\log 0.75}n>log0.75log0.01​.

[2]
b.

Find the smallest possible value of nnn.

[2]
c.

For this value of nnn, find the mean and the variance of XXX.

[1]
d.

For this value of nnn, find P(X≥4)P(X \ge 4)P(X≥4).

[2]
Markscheme

2.4 N: Statistical distributions Questions

  1. A Level
  2. /Maths
  3. /2.4 N: Statistical distributions

390 exam-style questions on AQA A Level Maths 2.4 N: Statistical distributions, covering 2.4.1 Discrete distributions and the binomial, 2.4.2 The Normal distribution (A-level only), and 2.4.3 Selecting an appropriate distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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