AQA A Level Further Maths Paper 3 Statistics June 2025 question paper

The continuous random variable X has standard deviation 16

Find Var(5X – 12)

Circle your answer.

80 400 6388 6400

The discrete random variable Y has probability distribution

Find the mode of Y

Circle your answer.

– 6 0.21 0.56 18

Find P(0.1 < X < 0.3)

Give your answer to three decimal places.

Show that the median of X is equal to

Find f(x), the probability density function of X

The discrete random variable D has a discrete uniform distribution taking values 1, 2, 3, …, n

The continuous random variable R has a rectangular distribution taking values between n and n + 1

The random variables D and R are independent.

Show that n = 16

Students are given a questionnaire asking them about their experiences while studying at their university.

Each student’s answers are used to calculate that student’s satisfaction score for their university.

The satisfaction scores, X, for a particular university are known to have a normal distribution.

A random sample of 11 students from the university is taken and their satisfaction scores are recorded. The summarised results are

Construct a 90% confidence interval for the population mean satisfaction score for the university.

Give your values to two decimal places.

The university claims that the mean satisfaction score is 90

Test the university’s claim, using the 10% level of significance.

A company sells a particular type of game.

In the game, a player can score 0, 10 or 100 points.

The probability of scoring 10 points is 0.37

The probability of scoring 100 points is 0.04

For a new edition of the game, the company is considering replacing the points scored per game X with Xⁿ, where n is a positive constant, while leaving the probabilities unchanged.

The company wants the mean score of the new edition to be equal to 50 times the mean score of the original game.

Find the possible points a player can score in the new edition.

Give your values to the nearest whole number.

A prototype of the new edition is produced for the company to assess.

For the new edition, the company now decides that it wants

the points scored changed so that they are all multiples of 10

the mean score to be at least 50 times the mean score of the original game.

State how your answer to part (a) can be refined.

In a village there are two coffee shops A and B, and two restaurants C and D

A random sample of 300 villagers is asked to state their favourite coffee shop and their favourite restaurant.

130 villagers said that their favourite coffee shop is A

160 villagers said that their favourite restaurant is D

88 villagers said that their favourite coffee shop is B and their favourite restaurant is C

Elaine claims that there is an association between favourite coffee shop and favourite restaurant.

Test Elaine’s claim, using the 5% level of significance.

A company sends out text messages to customers at random times during working hours.

The mean number of text messages sent per 30 minutes is 60

One text message being sent is independent of any other text message being sent.

The company sends text messages at a constant mean rate and sends them individually.

Using integration, show that the mean time between text messages being sent is 0.5 minutes.

Show that the probability that the company sends more than 130 text messages in an hour is 0.169, correct to three decimal places.

The company sends out text messages during a 7-hour interval on working days.

Find the probability that the company sends more than 130 text messages in an hour in exactly 2 of the 7 hours.

Give your answer to two decimal places.