OCR MEI Further Statistics Minor 2022 June — Question 6

Exam BoardOCR MEI
ModuleFurther Statistics Minor (Further Statistics Minor)
Year2022
SessionJune
TopicUniform Distribution
TypeArithmetic sequence uniform distribution
6 The random variable \(X\) has a uniform distribution over the values \(\{ 1,4,7 , \ldots , 3 n - 2 \}\), where \(n\) is a positive integer.
  1. Determine \(\operatorname { Var } ( X )\) in terms of \(n\).
  2. Given that \(n = 100\), find the probability that \(X\) is within one standard deviation of the mean.
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