OCR MEI S2 2008 January — Question 3

Exam BoardOCR MEI
ModuleS2 (Statistics 2)
Year2008
SessionJanuary
TopicNormal Distribution
TypeCombined events across distributions

3 In a large population, the diastolic blood pressure (DBP) of 5-year-old children is Normally distributed with mean 56 and standard deviation 6.5.
  1. Find the probability that the DBP of a randomly selected 5-year-old child is between 52.5 and 57.5. The DBP of young adults is Normally distributed with mean 68 and standard deviation 10.
  2. A 5-year-old child and a young adult are selected at random. Find the probability that the DBP of one of them is over 62 and the other is under 62.
  3. Sketch both distributions on a single diagram.
  4. For another age group, the DBP is Normally distributed with mean 82. The DBP of \(12 \%\) of people in this age group is below 62. Find the standard deviation for this age group.