Mathematics 9709 · AS & A Level · The normal distribution
The normal distribution — practice question
The amount of grapes sold each day by a large shop may be represented by a normal distribution with mean $28\text{ kg}$. On $10\%$ of days, the quantity sold is below $16\text{ kg}$.
(a)[3]
Find the standard deviation of the amount of grapes sold each day.
(b)[3]
A random selection of $12$ days is made. Find the probability that less than $16\text{ kg}$ of grapes are sold on more than $2$ of these $12$ days.
(c)[4]
In a random sample of $365$ days, how many days would you expect the mass of grapes sold to lie within $1.3$ standard deviations of the mean?
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Applies the correct standardisation $\frac{16-28}{\sigma}=-1.282$.” …