OCR MEI Further Statistics Major 2019 June — Question 3

Exam BoardOCR MEI
ModuleFurther Statistics Major (Further Statistics Major)
Year2019
SessionJune
TopicLinear combinations of normal random variables
TypeMixed sum threshold probability

3 The weights of bananas sold by a supermarket are modelled by a Normal distribution with mean 205 g and standard deviation 11 g .
  1. Find the probability that the total weight of 5 randomly selected bananas is at least 1 kg . When a banana is peeled the change in its weight is modelled as being a reduction of \(35 \%\).
  2. Find the probability that the weight of a randomly selected peeled banana is at most 150 g Andy makes smoothies. Each smoothie is made using 2 peeled bananas and 20 strawberries from the supermarket, all the items being randomly chosen. The weight of a strawberry is modelled by a Normal distribution with mean 22.5 g and standard deviation 2.7 g .
  3. Find the probability that the total weight of a smoothie is less than 700 g .