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CAIE A-Level Mathematics 5.5.2 Problems with a Normal Variable

Practise standardising a normal variable to calculate probabilities and expected frequencies or working backwards from a probability to determine an unknown mean, deviation or…

Syllabus
2028–2030
Course
Mathematics 9709
Level
A2

Exam points

  • write Z = (X − μ)/σ with each boundary substituted before consulting normal tables
  • combine Φ values or complementary tails to calculate an interval probability or expected count
  • convert a stated probability to its z-value and solve the resulting equation for μ, σ or a boundary

5.5.2—Problems concerning a variable X question 1

[Maximum number: 3]

The mass of grapes sold per day by a large shop can be modelled by a normal distribution with mean 28 kg . On 10 % of days less than 16 kg of grapes are sold.

Find the standard deviation of the mass of grapes sold per day.

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