Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
Before publication, a book of this kind is proofread and any mistakes are corrected. For costing, each error is put into one of two classes: minor or major. The numbers of minor and major errors in a book are represented by the independent distributions $N(380, 140)$ and $N(210, 80)$ respectively. Assume that no continuity corrections are required when these models are used.
One book of this type is selected at random.
(a)[5]
Find the probability that the number of minor errors is at least $200$ greater than the number of major errors.
(b)[5]
The correction costs for a minor error and a major error are $20$ cents and $50$ cents respectively. Find the probability that the total cost of correcting the errors in the book is less than $\$190$.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Correct mean $E(S-L)=170$ or $E(S-L-200)=-30$” …