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CAIE A Level Mathematics 9709

The normal distribution questions

Exam-style questions on The normal distribution, ordered from foundation to challenge. Pick one, write your answer the way you would in the exam, and it comes back marked against the mark scheme, point by point.

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Written by Markquill to follow the Cambridge International syllabus. Markquill is independent and is not affiliated with or endorsed by Cambridge International.

  1. 2 marksFoundationA random variable X is normally distributed with mean μ = 48 and standard deviation σ = 10. A value x = 98 is observed. Calculate the z-score for this value, defined as Z = (x - μ)/σ.
  2. 3 marksStandardThe random variable X is normally distributed with mean 100 and standard deviation 5. A particular value of X has standardised value z = 1.4.
  3. 3 marksStandardThe random variable X is normally distributed with mean 100 and unknown standard deviation σ. The value X = 109 has standardised value z = 0.5.
  4. 4 marksChallengeThe random variable X is normally distributed with mean μ = 90 and standard deviation σ = 2000. Find the value of x such that P(X < x) = 0.975.
  5. 4 marksChallengeThe random variable X follows a binomial distribution with 100 trials and probability of success 50\%. A normal approximation is used to estimate P(X leqslant 42).
  6. 4 marksChallengeThe random variable X is normally distributed with mean μ = 11 and unknown standard deviation σ. Given that P(X < 17) = 0.9332, find σ.
  7. 4 marksChallengeThe heights of a certain plant species are normally distributed with standard deviation 100 cm. It is known that P(X 1000) = 0.025. Find the mean height.