Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

In Jimpuri, the weights, in kilograms, of boys aged 16 years follow a normal distribution with mean 61.4 and standard deviation 12.3.
(i)[3]

Find the probability that a randomly selected boy aged 16 years in Jimpuri weighs more than 65 kilograms.

(ii)[4]

For boys aged 16 years in Jimpuri, $25\%$ have a weight between $65$ kilograms and $k$ kilograms, where $k$ is greater than $65$. Find $k$.

(iii)[5]

In Brigrville, the weights, in kilograms, of boys aged 16 years are normally distributed. $99\%$ of the boys weigh less than $97.2$ kilograms and $33\%$ of the boys weigh less than $55.2$ kilograms. Find the mean and standard deviation of the weights of boys aged 16 years in Brigrville.

Worked solution & mark scheme

This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: Accurate standardisation $P(Z>0.2927)$

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