Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The lengths of time a garage needs to attach a tow bar to a car are normally distributed with mean $m$ hours and standard deviation $0.35$ hours. It is given that $95\%$ of the times exceed $0.9$ hours.
(i)[3]
Find $m$.
(ii)[5]
On one day, $4$ cars are fitted with tow bars. Find the probability that none of them takes more than $2$ hours to fit.
(iii)[3]
The times in hours needed by another garage to fit a tow bar onto a car have the distribution $N(\mu, \sigma^2)$ where $\mu = 3\sigma$. Find the probability that it takes more than $0.6\mu$ hours to fit a tow bar onto a randomly selected car at this garage.
Worked solution & mark scheme
This 11-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Use the correct $z$-value $z=-1.645$.” …