Exam-Style Question on Probability
A mathematics exam-style question with a worked solution that can be revealed gradually
Question id: 340. This question is similar to one that appeared on an IB Standard paper in 2018. The use of a calculator is allowed.
The length of Costlow's bâtard bread loaves in centimetres is normally distributed with mean \( \mu \). The following table shows probabilities for values of \(L\).
|Length (\(L\))||\(L \lt 30\)||\(30 \le L \le 42\)||\(L \gt 42\)|
(a) Calculate the value of \(k\).
(b) Show that \( \mu \) = 36.
(c) Find P(\(L \gt 39\)).
The loaves are displayed in baskets of twelve. Any loaves with a length less than 31cm are classified as short.
(d) Find the probability that a basket of loaves selected at random contains at most one loaf that is short.
(e) Each Costlow supermarket has 40 baskets of loaves. One of the Costlow supermarkets is selected at random. Find the expected number of baskets in this supermarket that contain at most one loaf that is too short.
(f) Find the probability that at least 28 baskets in this supermarket contain at most one loaf that is too short.
The worked solutions to these exam-style questions are only available to those who have a Transum Subscription.
Subscribers can drag down the panel to reveal the solution line by line. This is a very helpful strategy for the student who does not know how to do the question but given a clue, a peep at the beginnings of a method, they may be able to make progress themselves.
This could be a great resource for a teacher using a projector or for a parent helping their child work through the solution to this question. The worked solutions also contain screen shots (where needed) of the step by step calculator procedures.
A subscription also opens up the answers to all of the other online exercises, puzzles and lesson starters on Transum Mathematics and provides an ad-free browsing experience.
Drag this panel down to reveal the solution
©1997 - 2021 Transum Mathematics :: For more exam-style questions and worked solutions go to Transum.org/Maths/Exam/