SPS SPS SM Statistics 2021 May — Question 4

Exam BoardSPS
ModuleSPS SM Statistics (SPS SM Statistics)
Year2021
SessionMay
TopicApproximating Binomial to Normal Distribution
TypeNormal approximation to normal-derived binomial

  1. A machine puts liquid into bottles of perfume. The amount of liquid put into each bottle, \(D \mathrm { ml }\), follows a normal distribution with mean 25 ml
Given that \(15 \%\) of bottles contain less than 24.63 ml
  1. find, to 2 decimal places, the value of \(k\) such that \(\mathrm { P } ( 24.63 < D < k ) = 0.45\) A random sample of 200 bottles is taken.
  2. Using a normal approximation, find the probability that fewer than half of these bottles contain between 24.63 ml and \(k \mathrm { ml }\)