(i)[5]
Find the proportions for large, small and medium pineapples.
(ii)[3]
Find the weight that is exceeded by the heaviest $5\%$ of pineapples.
(iii)[5]
Find the value of $k$ for which $\mathrm{P}(k < X < 610) = 0.3$.
Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The pineapple weight, measured in grams, is represented by the random variable $X$, and $X$ follows a normal distribution with mean $500$ and standard deviation $91.5$. Any pineapple with weight above $570$ grams is labelled ‘large’. Any pineapple with weight below $390$ grams is labelled ‘small’, while all others are labelled ‘medium’.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Standardising by means of $z=\frac{570-500}{91.5}$ or $\frac{390-500}{91.5}$” …
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