CAIE A-Level Mathematics 6.4.7 Confidence Intervals for a Population Mean

CAIE A-Level Mathematics 6.4.7 Confidence Intervals for a Population Mean
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise constructing and interpreting confidence intervals for a population mean using a known variance or large sample, an appropriate z-value and the standard error.

How this is tested

  • select the two-tailed standard-normal critical value for the stated confidence level
  • calculate the interval as x̄ ± zσ/√n, using an estimated deviation for a large sample
  • interpret confidence level, margin of error or interval width without treating μ as random

Question 1(a)

[Maximum number: 6]

A student notes the length，t minutes，of certain lectures．The results for a random sample of 80 lectures are summarised as follows．

n=80∑t=6430∑t2=519740n=80 \quad \sum t=6430 \quad \sum t^{2}=519740

（a）Calculate a 96\％confidence interval for the population mean length of the lectures．