The mass, in tonnes, of steel produced per day at a factory is normally distributed with mean 65.2 and
standard deviation 3.6. It can be assumed that the mass of steel produced each day is independent of
other days. The factory makes $50 profit on each tonne of steel produced.
Find the probability that the total profit made in a randomly chosen 7-day week is less than $22000.

Q: What topic does this question test?

This question tests Probability and statistics in A-Level Mathematics (syllabus code 9709). It is worth 6 marks.

Q: Which exam paper is this question from?

This question appeared in the Cambridge A-Level Mathematics May/June 2023 examination, Paper 6 Variant 3 (9709_s23_qp_63.pdf).

Question

The mass, in tonnes, of steel produced per day at a factory is normally distributed with mean 65.2 and
standard deviation 3.6. It can be assumed that the mass of steel produced each day is independent of
other days. The factory makes $50 profit on each tonne of steel produced.
Find the probability that the total profit made in a randomly chosen 7-day week is less than $22000.

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