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

  • Full mark scheme, point by point
  • Step-by-step worked solution
  • Write your answer & get it marked instantly by AI