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4.5.1 Statistical distributions (A-level only)

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Question 45

The random variable XXX is normally distributed with unknown mean μ\muμ and known variance σ2\sigma^2σ2. A random sample of nnn observations of XXX produced a 95%95\%95% confidence interval for μ\muμ of (12.42,12.85)(12.42, 12.85)(12.42,12.85).

a.

Show that the standard error used to find this confidence interval is 0.1100.1100.110 to 333 significant figures.

[3]
b.

Using the same random sample,

find a 98%98\%98% confidence interval for μ\muμ. Give your answers to 333 decimal places.

[4]
c.

The r%r\%r% confidence interval using the same random sample has a width of 0.500.500.50.

Calculate the value of rrr.

[4]

4.5.1 Statistical distributions (A-level only) Questions

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