OCR MEI Further Statistics Major Specimen — Question 5

Exam BoardOCR MEI
ModuleFurther Statistics Major (Further Statistics Major)
SessionSpecimen
TopicLinear combinations of normal random variables
TypeSingle sum threshold probability

5 A particular brand of pasta is sold in bags of two different sizes. The mass of pasta in the large bags is advertised as being 1500 g ; in fact it is Normally distributed with mean 1515 g and standard deviation 4.7 g . The mass of pasta in the small bags is advertised as being 500 g ; in fact it is Normally distributed with mean 508 g and standard deviation 3.3 g .
  1. Find the probability that the total mass of pasta in 5 randomly selected small bags is less than 2550 g .
  2. Find the probability that the mass of pasta in a randomly selected large bag is greater than three times the mass of pasta in a randomly selected small bag.