CAIE S1 2018 June — Question 2

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2018
SessionJune
TopicNormal Distribution
TypeDirect binomial from normal probability

2 The random variable \(X\) has the distribution \(\mathrm { N } \left( - 3 , \sigma ^ { 2 } \right)\). The probability that a randomly chosen value of \(X\) is positive is 0.25 .
  1. Find the value of \(\sigma\).
  2. Find the probability that, of 8 random values of \(X\), fewer than 2 will be positive.