Mathematics 9709 · AS & A Level · Continuous random variables

Continuous random variables — practice question

Video lengths for a particular popular song are normally distributed, with mean $3.9$ minutes. $18\%$ of the videos run for more than $4.2$ minutes.
(i)[3]

Find the standard deviation of the lengths of these videos.

(ii)[4]

Find the probability that a randomly chosen video has a length that is less than half a minute away from the mean.

(iii)[2]

Without doing any further calculation, determine whether $p$ is more than, equal to, or less than your answer in part (ii). You must give a reason for your decision.

(c(iii))[2]

Without doing any further calculation, decide whether $p$ is more than, equal to, or less than your answer to part (ii). You must explain how you reached your conclusion.

Worked solution & mark scheme

This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: Standardise using $z=\frac{4.2-3.9}{\sigma}$

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