Practice Paper Statistics 1 (Edexcel International AS Maths: Mechanics 1)

Practice Paper Questions

1a
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2 marks

The random variable X has the probability function

straight P open parentheses X equals x close parentheses equals space open curly brackets table attributes columnalign left end attributes row cell k x space space space space space space space space space space space space space space x equals 1 comma 3 comma 5 comma 7 end cell row cell 0 space space space space space space space space space space space space space space space space otherwise end cell end table close space

 Find the value of k.

1b
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2 marks

Find straight P left parenthesis X greater than 3 right parenthesis.

1c
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1 mark

State, with a reason, whether or not X is a discrete random variable.

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2a
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4 marks

A bag contains 12 orange marbles, 8 purple marbles and 5 red marbles.  A marble is taken from the bag and its colour is recorded, but it is not replaced in the bag.  A second marble is then taken from the bag and its colour is recorded.

Draw a tree diagram to represent this information.

2b
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4 marks

Find the probability that:

(i)
both marbles are different colours

(ii)
the second marble is purple, given that both marbles are different colours.

 

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3a
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3 marks

The Tell It Like It Is burger bar has been collecting data to find out whether customers like the restaurant’s two signature menu items – the Absolutely Awesome A-list Burger and the Basic But It’ll Do Bargain Burger.  The probability that a customer likes both burgers is 0.12.  The probability that a customer likes only one of the burgers is 0.71.  The probability that a customer likes the Basic But It’ll Do Bargain Burger but doesn’t like the Absolutely Awesome A-list Burger is 0.03.

Draw a Venn diagram to represent this information.

3b
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2 marks

Determine whether the events ‘likes the Absolutely Awesome A-list Burger’ and ‘likes the Basic But It’ll Do Bargain Burger’ are independent.

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4a
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3 marks

A machine is used to fill bottles of a particular brand of soft drink.  The volume, V ml, of soft drink in the bottles is normally distributed with mean 450 ml and standard deviation sigma  ml.  Given that 5% of the cans contain less than 429 ml of soft drink, find:

the value of sigma,

4b
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3 marks

P left parenthesis V greater or equal than 475 right parenthesis correct to 3 decimal places,

4c
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2 marks

the probability that the volume of a randomly selected bottle is no more than one standard deviation away from the mean.

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5a
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3 marks

Workers at an elephant sanctuary measure the health of their elephants by weighing the amount of dung (d space k g) each one produces.  The data for the mass of dung produced in one day by 18 elephants can be summarised as  capital sigmad= 895  and  straight capital sigmad2= 45 810.

Calculate the mean and variance of the amount of dung produced that day.

5b
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2 marks

To calculate how much food (f k g) to give each elephant, staff use the formula f= 3d – 25.

Calculate the mean and variance of the amount of food the workers should give to the elephants each day.

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6a
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3 marks

A teacher took 19 students on an international trip.  The incomplete box plot below shows part of the summary of the weights, in kg, of the luggage brought by each student.  Each student’s luggage weighed a different value.q2-hard-2-2-data-presentation-edexcel-a-level-maths-statistics

The median weight is 4 kg more than the lower quartile.  The range of weights is three times the interquartile range of weights.

Use the information above to complete the box plot.

6b
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2 marks

Calculate the proportion of luggage weights which were less than 20 kg.

6c
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2 marks

Students had to pay an additional fee if the weight of their luggage exceeded 23 kg.

Find the number of students who had to pay the additional fee.

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7a
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4 marks

Ms Chew is an accountant who is examining the length of time it takes her to complete jobs for her clients.  Ms Chew looks at her spreadsheet and lists the number of hours it took her to complete her last 12 jobs:

9 2 7 6 5 2 4 6 21 5 3 8

An outlier is an observation which lies more than  2 standard deviations away from the mean.

Show that 21 is the only outlier.

7b
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3 marks

Ms Chew looks at her handwritten records and finds that the value 21 was typed into the spreadsheet incorrectly.  It should have been 12.

Without further calculations, explain the effect this would have on the:

(i)
mean
(ii)
standard deviation
(iii)
median.

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8a
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4 marks

Effie loves watching the turtles play in the lake near her house, she thinks that there is a relationship between the number of turtles and the number of ducks that live on different parts of the lake.  She decides to investigate this further and gathers data on duck and turtle populations from six wildlife centres.  Effie records the data in the table below.

Centre

A

B

C

D

E

F

Ducks, bold italic d

6500

4000

6000

5500

3500

5500

Turtles, bold italic t

400

250

325

310

100

430

Effie codes the results using the codes x space equals fraction numerator d space minus space m over denominator n end fraction space and  y equals space fraction numerator t minus p over denominator q end fraction.  Some of the values for x and y are recorded in the table below.

Centre

A

B

C

D

E

F

 bold italic x

 

 

2

 

 

1.5

 bold italic y

1

 

 

 

 

1.2

Find the values of m comma space n comma space p and q hence, complete the table.

8b
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6 marks
(i)
Find the values of S subscript x x end subscript and S subscript x y end subscript.
(ii)
Hence, find the regression line of y on x.
8c
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3 marks

Use your answers to parts (a) and (b) to find the regression line of t on d, show your working clearly.

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9a
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1 mark

The discrete random variable X has the probability distribution shown in the following table: 

bold italic x negative 2 0 2 4 6
bold P stretchy left parenthesis X equals x stretchy right parenthesis p begin mathsize 16px style 2 over 15 end style begin mathsize 16px style 1 fourth end style begin mathsize 16px style 2 over 15 end style p

  

Without working out the value of p, explain why straight E open parentheses X close parentheses space equals space 2.

9b
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1 mark

find the value of p.

9c
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2 marks

Find Var open parentheses straight X close parentheses.

9d
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2 marks

The outcome of a random variable Y is double the outcome of X

Complete the probability distribution for Y below: 

bold y negative 4 0 4 8

 

bold P begin bold style stretchy left parenthesis Y equals y stretchy right parenthesis end style

 

begin mathsize 16px style 2 over 15 end style

 

 

 

 

9e
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2 marks

Find P left parenthesis Y greater than X right parenthesis.

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10a
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4 marks

The test scores, X, of a group of Royal Navy recruits in an aptitude test are modelled as a normal distribution with  X tilde N left parenthesis 520 comma space 89.9 squared right parenthesis.

Find the interquartile range of the scores.

10b
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5 marks

Those who get a score over 670 are offered a role within the submarine service.  Only those who get a score over 750 are offered a leadership role within the submarine service.

Given that Mervyn, one of the recruits, has been offered a role within the submarine service, find the probability that he is offered a leadership role.

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