Edexcel S3 2022 June — Question 6

Exam BoardEdexcel
ModuleS3 (Statistics 3)
Year2022
SessionJune
TopicLinear combinations of normal random variables
TypeMixed sum threshold probability

6 A particular lift has a maximum load capacity of 700 kg .
The weights of men are normally distributed with mean 80 kg and standard deviation 10 kg . The weights of women are normally distributed with mean 69 kg and standard deviation 5 kg . You may assume that weights of people are independent.
  1. Find the probability that when 6 men and 3 women are in the lift, the load exceeds 700 kg . A sign in the lift states: "Maximum number of people in the lift is \(c\) "
  2. Find the value of \(c\) such that the probability of the load exceeding 700 kg is less than \(2.5 \%\) no matter the gender of the occupants.