Turn on thread page Beta
 You are Here: Home >< Maths

# S2 questions watch

1. S2 Heinemann exercise 3B

(8) In a multiple choice examination candidate jones picks his answers to each question at random from a list of 3 answers provided, of which only one is correct. A candidate passing 18 or more questions coreectly passes the examination (a) For paper containing 45 questions use normal approx to find prob that jones passes (b) It is required that prob that Jones passes shouls be less than 0.005. Use normal approx to show paper should contain at most 31 questions

exercise 2D
9- Mode of a continous random variable X is 1 and this is a stationary point. Given that X takes values over the range [0,3] find possible expressions for (a) C.D.F of x AND (b) p.d.f of X
2. (8)
(a)
X
= Number of correct answers
~ Bin(45, 1/3)

Approximately,

X
~ N(45*(1/3), 45*(1/3)*(2/3))
= N(15, 10)

Using a continuity correction,

P(Jones passes)
= P(X >= 18)
P(N(15, 10) >= 17.5)
= 1 - Phi(2.5/sqrt(10))
= 0.215

(b)
P(Jones passes if there are 32 questions)
P(N(32*(1/3), 32*(1/3)*(2/3)) >= 17.5)
= P(N(32/3, 64/9) >= 17.5)
= 1 - Phi((17.5 - 32/3) / sqrt(64/9))
= 0.00520
> 0.005

P(Jones passes if there are 31 questions)
P(N(31*(1/3), 31*(1/3)*(2/3)) >= 17.5)
= P(N(31/3, 62/9) >= 17.5)
= 1 - Phi((17.5 - 31/3) / sqrt(62/9))
= 0.00316
< 0.005

Therefore the test must contain at most 31 questions.

Turn on thread page Beta

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: June 10, 2005
The home of Results and Clearing

### 1,196

people online now

### 1,567,000

students helped last year
Today on TSR

### A-level results day chat: 2 days to go!

Chat about results here

### University open days

1. SAE Institute
Animation, Audio, Film, Games, Music, Business, Web Further education
Thu, 16 Aug '18
2. Bournemouth University
Clearing Open Day Undergraduate
Fri, 17 Aug '18
3. University of Bolton
Fri, 17 Aug '18
Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE