AQA A Level Further Maths Paper 3S June 2024 question paper 7367/3S

The random variable X has a Poisson distribution with mean 16

Find the standard deviation of X

Circle your answer.

4 8 16 256

Find the median of Y

Circle your answer.

Research has shown that the mean number of volcanic eruptions on Earth each day is 20

Sandra records 162 volcanic eruptions during a period of one week.

Sandra claims that there has been an increase in the mean number of volcanic eruptions per week.

Test Sandra’s claim at the 5% level of significance.

Show that the mean of X is (In 27 – 2)

Over time it has been accepted that the mean retirement age for professional baseball players is 29.5 years old.

Imran claims that the mean retirement age is no longer 29.5 years old.

He takes a random sample of 5 recently retired professional baseball players and records their retirement ages, x. The results are

State an assumption that you should make about the distribution of the retirement ages to investigate Imran’s claim.

Investigate Imran’s claim, using the 10% level of significance.

State the variance of X

Hence find the variance of Y

Fully justify your answer.

The discrete random variable X has probability distribution

Show that P(X ≤ 17 │ X > E(X)) = 0.75

A company owns three shops, A, B and C, which are based in different towns.

Each shop gives a questionnaire to 250 of their customers, and every customer completes the questionnaire.

One of the questions asks whether the customer rates the shop as good, satisfactory or poor.

For shop A, 26% of customers rate the shop as good and 38% of customers rate the shop as poor.

For shop B, 32% of customers rate the shop as good and 40% of customers rate the shop as satisfactory.

Altogether, there are 210 good ratings and 261 satisfactory ratings.

Complete the following table with the observed frequencies.

Carry out a test for association between shop and rating, using the 1% level of significance.

Construct a 91% confidence interval for the population mean length of the shark teeth.

Give your limits to two decimal places.

The random sample is used to carry out a hypothesis test using the 9% level of significance. The hypotheses are H₀: μ = 10.36 H₁: μ ≠ 10.36

State, with a reason, whether the null hypothesis will be rejected.

The hypothesis test is repeated with a second random sample of 250 teeth which also has s = 1.3 cm

Find the power of this test assuming that the population mean length of the shark teeth is 10.32 cm

Give your answer to two decimal places.