CAIE S1 2006 June — Question 3

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2006
SessionJune
TopicNormal Distribution
TypeIndependent events across days/trials

3 The lengths of fish of a certain type have a normal distribution with mean 38 cm . It is found that \(5 \%\) of the fish are longer than 50 cm .
  1. Find the standard deviation.
  2. When fish are chosen for sale, those shorter than 30 cm are rejected. Find the proportion of fish rejected.
  3. 9 fish are chosen at random. Find the probability that at least one of them is longer than 50 cm .