Binomial Distribution 2

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From users who are members of MASH Bath: Question Bank :

Ruth Hand

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Ready to use

3 years, 8 months ago

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Christian Lawson-Perfect 2 years, 6 months ago

Published this.

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Ruth Hand 3 years, 8 months ago

Gave some feedback: Ready to use

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Ben McGovern 4 years, 2 months ago

Created this as a copy of Probability: Binomial Distribution 1.

Name	Status	Author	Last Modified
Probability: Binomial Distribution 1	Ready to use	Ben McGovern	27/09/2022 09:01
Binomial Distribution 2	Ready to use	Ben McGovern	27/09/2022 09:01

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Question statement

A commuter gets a train each weekday morning, and {n} out of 5 days the train is delayed.

Give any introductory information the student needs.

			Name	Type	Generated Value

n	integer	1
sol2	rational	181/3125
sol1	rational	1024/3125
partb	string	<p>If the train is delayed mor
b1	string	<p>If the train is delayed mor
b2	string	<p>If the train is delayed mor
prob	rational	1/5
numd	integer	2

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(1,2,3,4)

JME function reference

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

→ Used by:

prob

Statement

Parts

Information only
Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Gap 1 Number entry
  Add

Information only

Ask the student a question, and give any hints about how they should answer this part.

What is the probability that,

Advice

The answers involve binomial distributions because there are only 2 cases - the train is either delayed or it is not.

Therefore, we want to apply the binomial distribution

$P(X=r) =\, ^nC_r \, p^r \, (1-p)^{n-r}.$

Let $X$ be the number of days a train is delayed in a week.

Part (a):

$\begin{split} P(X=0) &\,= \binom{5}{0} \times \var{prob}^0 \times \var{1-prob}^5 \\ &\,= \var{1-prob}^5 \\ &\,= \var{sol1}. \end{split}$

Part (b):

{partb}

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Part	Test	Passed?
Information only
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Number entry
Number entry		Hasn't run yet

This question is used in the following exams:

Binomial distribution by Ruth Hand in MASH Bath: Moodle quizzes and TS.
Week 8 Probability II by Peter Chapman in Peter's workspace.
STAT7007 Assessment 2024 by Paula Harrison in STAT7007.

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Taxonomy: mathcentre

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Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 2 years, 6 months ago

Ruth Hand 3 years, 8 months ago

Ben McGovern 4 years, 2 months ago

Error in variable testing condition

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Generated value: `integer`

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Binomial Distribution 2

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 6 months ago

Ruth Hand 3 years, 8 months ago

Ben McGovern 4 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Information only

Generated value: `integer`