CAIE A-Level Mathematics 6.4.5 Sample mean

CAIE A-Level Mathematics 6.4.5 Sample mean
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise deciding when the Central Limit Theorem is needed and using an approximate normal model for large-sample means.

How this is tested

  • explain that CLT is needed when the population distribution is unknown or not normal
  • use sample size in the standard error when finding probabilities for X̄
  • state which part of a confidence interval or test uses the normal z-value

Question 3(b)

[Maximum number: 1]

The times, in minutes, taken by students to complete a test have mean μ\mu and standard deviation σ\sigma. The times taken by a random sample of 100 students are noted and are used to calculate a 95% confidence interval for μ\mu.

The calculation of the confidence interval required the use of the Central Limit theorem.

Explain why it is valid to use the Central Limit theorem in this case.