# Exam-Style Question on Normal Distribution

## A mathematics exam-style question with a worked solution that can be revealed gradually

##### List Of QuestionsExam-Style QuestionMore Normal QuestionsMore on this Topic

Question id: 698. This question is similar to one that appeared on an IB AA Higher paper in 2021. The use of a calculator is allowed.

The travelling times by train, $$T$$ minutes, between two towns can be modelled by a normal distribution with a mean of 55 minutes and a standard deviation of $$\sigma$$ minutes.

(a) Given that 8% of the times are longer than 68 minutes, find the value of $$\sigma$$.

(b) Find the probability that a randomly selected train journey will have a duration of more than 75 minutes.

(c) Given that a train journey between the two towns takes longer than an hour, find the probability that it takes less than 70 minutes.

On a particular day, there are 42 trains scheduled to travel between these two towns.

(d) Find the expected number of train journeys that will have a duration of more than an hour.

(e) Find the probability that more than 10 of the journeys on this particular day will have a duration of more than one hour.

 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.

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The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

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First, describe the content structure you found in 1-2 sentences.

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# Exam-Style Question on Normal Distribution

## A mathematics exam-style question with a worked solution that can be revealed gradually

##### List Of QuestionsExam-Style QuestionMore Normal QuestionsMore on this Topic

Question id: 698. This question is similar to one that appeared on an IB AA Higher paper in 2021. The use of a calculator is allowed.

The travelling times by train, $$T$$ minutes, between two towns can be modelled by a normal distribution with a mean of 55 minutes and a standard deviation of $$\sigma$$ minutes.

(a) Given that 8% of the times are longer than 68 minutes, find the value of $$\sigma$$.

(b) Find the probability that a randomly selected train journey will have a duration of more than 75 minutes.

(c) Given that a train journey between the two towns takes longer than an hour, find the probability that it takes less than 70 minutes.

On a particular day, there are 42 trains scheduled to travel between these two towns.

(d) Find the expected number of train journeys that will have a duration of more than an hour.

(e) Find the probability that more than 10 of the journeys on this particular day will have a duration of more than one hour.

 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

The exam-style questions appearing on this site are based on those set in previous examinations (or sample assessment papers for future examinations) by the major examination boards. The wording, diagrams and figures used in these questions have been changed from the originals so that students can have fresh, relevant problem solving practice even if they have previously worked through the related exam paper.

The solutions to the questions on this website are only available to those who have a Transum Subscription.

Exam-Style Questions Main Page

Search for exam-style questions containing a particular word or phrase:

To search the entire Transum website use the search box in the grey area below.
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The text passage contains an exam-style question on normal distribution with multiple parts, and it mentions the availability of worked solutions for subscribers.

TYPE: MULTIPLE_QUESTIONS