Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
The rod lengths manufactured by a company are normally distributed with mean $55.6\text{ mm}$ and standard deviation $1.2\text{ mm}$.
(a)[4]
From a random sample of $400$ of these rods, how many would you expect to be shorter than $54.8\text{ mm}$?
(b)[3]
Determine the probability that a rod selected at random from this company has a length lying within half a standard deviation of the mean.
Worked solution & mark scheme
This 7-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Using $Z=\dfrac{54.8-55.6}{1.2}$ to standardise, or an equivalent method with an allowable continuity correction” …