Year 12 AS Applied Exam 2022
Section A: Statistics
Total 60 marks, 1 hour 15 minutes
Topic List
•Statistics: (30 marks)
1. AS: Chapter 1-6.1 (Discrete Random Variables)
2. A2: Chapter 2 Conditional Probability
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Year 12 AS Applied Exam 2022
Section A: Statistics
Total 60 marks, 1 hour 15 minutes
Topic List
- Statistics: (30 marks)
- AS: Chapter 1-6.1 (Discrete Random Variables)
- A2: Chapter 2 Conditional Probability
Section A: Statistics
David uses the large data set to investigate the Daily Total Rainfall, r mm, for Cambourne. (a) Write down how a value of 0 < r ≤ 0 .05 is recorded in the large data set. (^) (1)
David uses the data for the 31 days of August 2015 for Cambourne and calculates the following statistics:
n = 31 X^ r = 174. 9 X^ r^2 = 3523. 283
(b) Use these statistics to calculate (i) the mean of the Daily Total Rainfall in Cambourne for August 2015, (ii) the standard deviation of the Daily Total Rainfall in Cambourne for August 2015. (3) David believes that the mean Daily Total Rainfall in August is less in the South than in the North of the UK. The mean Daily Total Rainfall in Leuchars for August 2015 is 1.72 mm to 2 decimal places. (c) State, giving a reason, whether this provides evidence to support David’s belief. (^) (2)
The mass, x grams of 800 apples are summarised in the histogram.
Use linear interpolation to estimate the median mass of the apples. (4)
(Total for question = 4 marks)
(Total for question = 6 marks)
The Venn diagram shows the events A, B and C and their associated probabilities, where p and q are probabilities.
(a) Find P (B) (^) (1)
(b) Determine whether or not A and B are independent. (^) (2)
Given that P (C|B) = P (C), (c) find the value of p and the value of q (^) (3)
The event D is such that
- A and D are mutually exclusive
- P (B ∩ D) > 0
(d) On the Venn diagram show a possible position for the event D
(1)
In a sixth form college,
- 60% of students study Mathematics.
- 30% of students study Languages.
- 20% of Mathematics students study Languages A student is chosen at random. (a) Given that the student studies Languages, find the probability that the student studies Mathematics. (^) (2)
(b) Given that the student does not study Mathematics, find the probability that the student studies Languages. (^) (3) (c) Find the probability that the randomly chosen student studies Mathematics but not Languages. (^) (2)