Mathematics 9709 · AS & A Level · Continuous random variables
Continuous random variables — practice question
Banana weights in a fruit shop are normally distributed with mean $150$ grams and standard deviation $50$ grams. Bananas are sold in three sizes: Small: less than $95$ grams; Medium: from $95$ grams to $205$ grams; Large: more than $205$ grams.
(i)[3]
Determine the proportion of bananas that are small.
(ii)[3]
Determine the weight exceeded by $10\%$ of bananas.
(iii(a))[1]
Banana prices are $10$ cents for a small banana, $20$ cents for a medium banana and $25$ cents for a large banana. Show that the probability a banana chosen at random costs $20$ cents is $0.7286$.
(iii(b))[3]
Work out the expected total cost of $100$ bananas chosen at random.
Worked solution & mark scheme
This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Express $P(X<95)$ in standard form as $P\left(Z<\tfrac{95-150}{50}\right)$” …