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2 Statistics

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Question 229

A commercial bakery produces two types of loaves: Sourdough and Rye. The weights of Sourdough loaves, SSS grams, and Rye loaves, RRR grams, are independently normally distributed such that

S∼N(820,152)andR∼N(780,122) S \sim \text{N}(820, 15^2) \quad \text{and} \quad R \sim \text{N}(780, 12^2) S∼N(820,152)andR∼N(780,122)
a.

Find the probability that the weights of 2 randomly selected Sourdough loaves will differ by more than 20 g.

[3]
b.

Find the probability that the weight of a randomly selected Rye loaf is less than 0.95 of the weight of a randomly selected Sourdough loaf.

[3]
c.

Loaves are packed into crates. Each crate contains either 10 randomly selected Sourdough loaves or 10 randomly selected Rye loaves. The weight of an empty crate has distribution N(1500,302)\text{N}(1500, 30^2)N(1500,302).

Find the probability that a full crate of Sourdough loaves weighs at least 450 g more than a full crate of Rye loaves.

[4]
Markscheme

2 Statistics Questions

  1. A Level
  2. /Maths
  3. /2 Statistics

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