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4.5.1 Statistical distributions (A-level only)

4.5.1 Statistical distributions (A-level only)

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Question 142

The random variable XXX is normally distributed with unknown mean μ\muμ and known variance σ2\sigma^2σ2. A random sample of 16 observations of XXX produced a 95%95\%95% confidence interval for μ\muμ of (40.04,43.96)(40.04, 43.96)(40.04,43.96).

a.

Find the mean of the sample.

[2]
b.

Show that the standard deviation σ\sigmaσ is 4.

[3]
c.

The a%a \%a% confidence interval using the 16 observations has a width of 3.3.

Calculate the value of aaa.

[4]
d.

Find the smallest sample size, of observations from XXX, that would be required to obtain a 95%95\%95% confidence interval for μ\muμ of width at most 2.5.

[3]
Markscheme

4.5.1 Statistical distributions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /4.5.1 Statistical distributions (A-level only)

228 exam-style questions on CCEA A Level Maths 4.5.1 Statistical distributions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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