Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

Adult female giraffe weights follow a normal distribution with mean $830\text{ kg}$ and standard deviation $120\text{ kg}$.
(i)[4]

A certain game reserve contains $430$ adult female giraffes. Determine how many of these adult female giraffes are expected to have a weight below $700\text{ kg}$.

(ii)[3]

If $90\%$ of adult female giraffes have weights between $(830 - w)\text{ kg}$ and $(830 + w)\text{ kg}$, determine the value of $w$.

(iii)[3]

Adult male giraffe weights are normally distributed with mean $1190\text{ kg}$ and standard deviation $\sigma\text{ kg}$. If $83.4\%$ of adult male giraffes weigh above $950\text{ kg}$, determine $\sigma$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Standardises $P(X<700)$ to give $Z<-1.083$

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