Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
In one country, winter daily minimum temperature, measured in $^\circ\text{C}$, follows the distribution $N(8, 24)$. Find the probability that a winter day chosen at random in this country has a minimum temperature from $7^\circ\text{C}$ to $12^\circ\text{C}$. In another country, the winter daily minimum temperature, in $^\circ\text{C}$, has a normal distribution with mean $\mu$ and standard deviation $2\mu$.
(i)[3]
Find the probability that a winter day chosen at random in this country has a minimum temperature between $7^\circ\text{C}$ and $12^\circ\text{C}$.
(ii)[2]
Find the proportion of winter days for which the minimum temperature is below zero.
(iii)[3]
$70$ winter days are selected at random. Find the expected number that have a minimum temperature which is more than three times the mean.
(iv)[3]
The probability that the minimum temperature is above $6^\circ\text{C}$ on any winter day is $0.0735$. Find the value of $\mu$.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct standardisation giving $z_1=\dfrac{12-8}{\sqrt{24}}$” …