Interval probability P(a < X < b)

Questions asking for the probability that X lies between two values, requiring two standardisations and subtraction of cumulative probabilities.

3 questions · Easy -1.1

2.04e Normal distribution: as model N(mu, sigma^2)2.04f Find normal probabilities: Z transformation
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CAIE S1 2012 June Q1
3 marks Easy -1.2
1 It is given that \(X \sim \mathrm {~N} ( 28.3,4.5 )\). Find the probability that a randomly chosen value of \(X\) lies between 25 and 30 .
CAIE S1 2014 June Q1
4 marks Moderate -0.8
1 The petrol consumption of a certain type of car has a normal distribution with mean 24 kilometres per litre and standard deviation 4.7 kilometres per litre. Find the probability that the petrol consumption of a randomly chosen car of this type is between 21.6 kilometres per litre and 28.7 kilometres per litre.
Edexcel S1 2004 January Q2
7 marks Easy -1.2
2. The random variable \(X\) is normally distributed with mean \(\mu\) and variance \(\sigma ^ { 2 }\).
  1. Write down 3 properties of the distribution of \(X\). Given that \(\mu = 27\) and \(\sigma = 10\)
  2. find \(\mathrm { P } ( 26 < X < 28 )\).