Practice Paper 3 (Statistics) (Edexcel A Level Maths: Statistics)

Practice Paper Questions

1a
Sme Calculator
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.

1b
Sme Calculator
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.

 

Did this page help you?

2a
Sme Calculator
1 mark

The incomplete box plot below shows data from the large data set regarding cloud cover between May and October 2015 in Cambourne.  Cloud cover is measured in Oktas on a scale from 0 (no cloud cover) to 8 (full cloud cover).q6a-easy-2-3-working-with-data-edexcel-a-level-maths-statistics

Find the interquartile range.

2b
Sme Calculator
3 marks

An outlier is defined as any data value that falls either more than
1.5 cross times (interquartile range) above the upper quartile or less than
1.5 cross times (interquartile range) below the lower quartile.

(i)
Find the boundaries (fences) at which outliers are defined.

(ii)
Explain why, using your knowledge of how cloud cover is measured in the large data set, there cannot be any high valued outliers.

2c
Sme Calculator
2 marks

Complete the box plot given that, where appropriate, the maximum and minimum values should be located at the boundaries (fences) at which outliers are defined.
(You are not required to mark any outliers on the box plot.)

Did this page help you?

3
Sme Calculator
7 marks

Students at two Karate Schools, Miyagi Dojo and Cobra Kicks, measured the force of a particular style of hit.  Summary statistics for the force, in newtons, with which the students could hit are shown in the table below:

  bold italic n bold capital sigma bold italic x bold capital sigma bold italic x to the power of bold 2
Miyagi Dojo 12 21873 41532545
Cobra Kicks 17 29520 52330890

(i)
Calculate the mean and standard deviation for the forces with which the students could hit.

(ii)
Compare the distributions for the two Karate Schools.

Did this page help you?

4a
Sme Calculator
4 marks

On 21st January 2020, doctors in China started recording and reporting the number of new daily cases of an unknown virus. The doctors record the number of new cases, c, of the virus and the number of days, d, after 21st January 2020.

d 1 2 3 4 5 6
c 278 48 221 92 277 x



d 7 8 9 10 11 12
c 700 1700 1600 1700 y 1500


The value of the product moment correlation coefficient between the number of days after 21
st January 2020 and the number of new cases was calculated as  r = 0.900.  

The table below gives the critical values, for different significance levels, of the product moment correlation coefficient,  r, for a sample size of 12. 

One tail 10% 5% 2.5% 1% 0.5%
n = 12 0.3981 0.4973 0.5760 0.6581 0.7079

 

(i)
Clearly stating suitable null and alternative hypotheses, show that there is evidence of linear correlation between the number of days and the number of new cases at a 1% level of significance.  

(ii)
Give a reason why a linear regression line is suitable to model the relationship between the number of days and the number of new cases reported each day.
4b
Sme Calculator
4 marks

The equation for the regression line of c on d is found to be  c = 184.58d – 266.39.

(i)
Use the regression line to estimate the number of new cases on the 6th and 11th day. 

(ii)
Explain why the equation for the regression line should not be used to estimate how many new cases there were on 19th January 2020.  

Did this page help you?

5a
Sme Calculator
2 marks

In the town of Edinboro, Pennsylvania, a festival of trimmed below the forehead hairstyles is held every year, known as the Edinboro Fringe Festival.  It is known that 70% of the residents of the town are in favour of the festival because of the tourism revenue it brings in.  The other 30% of residents oppose the festival because of the sometimes hostile reactions of the large number of tourists who arrive every year thinking they had actually made bookings to attend another well-known fringe festival.

25 residents are chosen at random by a local newspaper reporter.  Let the random variable X represent the number of those 25 residents that are in favour of the festival.

Suggest a suitable distribution for and comment on any necessary assumptions.

 

5b
Sme Calculator
3 marks

Find the probability that

(i)
76% or more of the residents chosen are in favour of the festival

(ii)
more of the residents chosen oppose the festival than are in favour of it.
5c
Sme Calculator
2 marks

The reporter knows that the chance of k or more of the 25 residents being opposed to the festival is less than 0.5%, where k is the smallest possible value that makes that statement true.

Find the value of k.

Did this page help you?

6a
Sme Calculator
1 mark

The weight of an adult pig can be modelled using a normal distribution with a mean of 255 kg and a variance of 2000 kg². A pig is labelled as supersized if it weighs more than 350 kg.

Using the model, find the probability that a randomly selected pig is labelled as supersized. Give your answer to four decimal places.

6b
Sme Calculator
4 marks

Ramon, a farmer, believes that the probability that his pigs are supersized is higher than the probability given by the model.  To test his belief Ramon randomly selects 12 pigs that he has owned and finds that two of them were classed as supersized.

Stating your hypotheses clearly, test Ramon’s belief using a 5% level of significance.

6c
Sme Calculator
4 marks

Ramon also claims that the mean weight of the pigs on his farm is higher than the mean weight according to the model.  Using the 12 pigs in his sample, Ramon calculates the sample mean as 273 kg.

Stating your hypotheses clearly, test Ramon’s claim using a 5% level of significance.

6d
Sme Calculator
2 marks

What do the results from parts (b) and (c) suggest about the variance of the weights of the pigs on Ramon’s farm? Explain your answer.

Did this page help you?

7a
Sme Calculator
2 marks

In January of 2021, the UK government announced a nationwide lockdown to control the spread of the coronavirus.  The table below shows the means and standard deviations of the average amounts of time spent indoors per day by some people in London, UK and in Wellington, New Zealand, in January of 2021.

  Number of people Mean (hr) Standard deviation
London 25 20.9 1.51
Wellington 15 15.1 2.87

Suggest a reason, in the context of the question, for why

(i)
the mean in London is higher than the mean in Wellington

(ii)

the standard deviation in London is lower than the standard deviation in Wellington.
7b
Sme Calculator
1 mark

Based on the data in the table, do you think the government in New Zealand had imposed the same restrictions as those in the UK?  Give a reason for your answer.

Did this page help you?