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

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).

Find the interquartile range.

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

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.)

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:

Miyagi Dojo	12	21873	41532545
Cobra Kicks	17	29520	52330890

On 21^st 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 21^st January 2020.

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. 

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

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  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.

Find the probability that

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

Find the value of .

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.

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.

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.

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.

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.

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

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.