Edexcel S2 2023 June — Question 1

Exam BoardEdexcel
ModuleS2 (Statistics 2)
Year2023
SessionJune
TopicApproximating Binomial to Normal Distribution
TypeCombined binomial and normal events

  1. In a large population \(40 \%\) of adults use online banking.
A random sample of 50 adults is taken.
The random variable \(X\) represents the number of adults in the sample that use online banking.
  1. Find
    1. \(\mathrm { P } ( X = 26 )\)
    2. \(\mathrm { P } ( X \geqslant 26 )\)
    3. the smallest value of \(k\) such that \(\mathrm { P } ( X \leqslant k ) > 0.4\) A random sample of 600 adults is taken.
    1. Find, using a normal approximation, the probability that no more than 222 of these 600 adults use online banking.
    2. Explain why a normal approximation is suitable in part (b)(i)