CAIE S1 2019 June — Question 7

Exam BoardCAIE
ModuleS1 (Statistics 1)
Year2019
SessionJune
TopicNormal Distribution
TypeMixed calculations with boundaries

7 The weight of adult female giraffes has a normal distribution with mean 830 kg and standard deviation 120 kg .
  1. There are 430 adult female giraffes in a particular game reserve. Find the number of these adult female giraffes which can be expected to weigh less than 700 kg .
  2. Given that \(90 \%\) of adult female giraffes weigh between \(( 830 - w ) \mathrm { kg }\) and \(( 830 + w ) \mathrm { kg }\), find the value of \(w\).
    The weight of adult male giraffes has a normal distribution with mean 1190 kg and standard deviation \(\sigma \mathrm { kg }\).
  3. Given that \(83.4 \%\) of adult male giraffes weigh more than 950 kg , find the value of \(\sigma\).