Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
The lifetimes, measured in hours, of one particular kind of light bulb are normally distributed with mean $2000$ hours and standard deviation $\sigma$ hours. The probability that a light bulb chosen at random from this type lasts for more than $1800$ hours is $0.96$.
(i)[3]
Find $\sigma$'s value.
(ii)[4]
A new type of light bulb has been developed using new technology. It is found that, on average, one in five of these new light bulbs lasts for more than 2500 hours. For a random sample of 300 of these new light bulbs, use a suitable approximate distribution to determine the probability that fewer than 70 last for more than 2500 hours.
(iii)[1]
Justify the use of the approximate distribution you chose in part (ii).
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme.