Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
A farmer trades eggs. Their weights, measured in grams, are modelled by a normal distribution with mean $80.5$ and standard deviation $6.6$. The eggs are sorted into small, medium or large by weight. An egg is small if it weighs below $76$ grams, and $40\%$ of the eggs fall into the medium category.
(a)[3]
State the percentage of eggs that are classified as small.
(b)[3]
State the least possible weight of an egg classified as large.
(c)[5]
Use an approximation to determine the probability that more than $68$ of these eggs were classified as medium.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Accurate standardisation: $P(X<76)=P(Z<\frac{76-80.5}{6.6})$.” …