Practice Paper Statistics 1 (Edexcel International A Level Maths: Pure 1)

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.

Find the probability that:

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.

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

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

the value of ,

correct to 3 decimal places,

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

Workers at an elephant sanctuary measure the health of their elephants by weighing the amount of dung () each one produces.  The data for the mass of dung produced in one day by 18 elephants can be summarised as  = 895  and  ²= 45 810.

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

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

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

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.

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.

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

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.

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:

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

Show that 21 is the only outlier.

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:

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.

Effie codes the results using the codes  and  .  Some of the values for  and  are recorded in the table below.

Centre	A	B	C	D	E	F
			2			1.5
	1					1.2

Find the values of  and hence, complete the table.

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

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

Without working out the value of , explain why

find the value of .

Find .

The outcome of a random variable  is double the outcome of . 

Complete the probability distribution for  below: 

			4	8

Find .

The test scores, , of a group of Royal Navy recruits in an aptitude test are modelled as a normal distribution with  .

Find the interquartile range of the scores.

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.