CAIE S2 2022 June — Question 6

Exam BoardCAIE
ModuleS2 (Statistics 2)
Year2022
SessionJune
TopicLinear combinations of normal random variables
TypeDirect comparison of two variables

6 The masses, in kilograms, of large and small sacks of grain have the distributions \(\mathrm { N } ( 53,11 )\) and \(\mathrm { N } ( 14,3 )\) respectively.
  1. Find the probability that the mass of a randomly chosen large sack is greater than four times the mass of a randomly chosen small sack.
  2. A lift can safely carry a maximum mass of 1000 kg . Find the probability that the lift can safely carry 12 randomly chosen large sacks and 25 randomly chosen small sacks.
    \(7 X\) is a random variable with distribution \(\operatorname { Po } ( 2.90 )\). A random sample of 100 values of \(X\) is taken. Find the probability that the sample mean is less than 2.88 .
    If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.