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2.4.12 Calculate probabilities from a Normal distribution (A-level only)

2.4.12 Calculate probabilities from a Normal distribution (A-level only)

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Question 51

A bakery produces loaves of bread whose weights, WWW grams, follow a normal distribution with mean 800 g800\text{ g}800 g and standard deviation 25 g25\text{ g}25 g.

a.

Estimate the proportion of loaves that weigh more than 840 g840\text{ g}840 g.

[2]
b.

The bakery classifies loaves into three categories: Small, Standard, and Large, such that there is an equal proportion of loaves (exactly 13\frac{1}{3}31​) in each category.

Find the weight limits that define the 'Standard' category.

[3]
c.

A loaf is selected at random from the 'Large' category.

Find the probability that this loaf weighs less than 830 g830\text{ g}830 g.

[3]
d.

A customer selects a random sample of 3 loaves from the bakery's total production.

Find the probability that there is exactly one loaf from each of the three categories.

[2]
Markscheme

2.4.12 Calculate probabilities from a Normal distribution (A-level only) Questions

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149 exam-style questions on OCR (MEI) A Level Maths 2.4.12 Calculate probabilities from a Normal distribution (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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