# WST01 Statistics 1 (S1) January 2023 Paper 01

Pearson Edexcel International A Level WST01 Statistics 1 (S1) past paper 01, January 2023. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wst01/2023-january-paper-01/
- PDF: https://mathvsarham.com/papers/wst01/WST01_january_2023_paper_01_qp.pdf
- Board: Edexcel
- Qualification: Pearson Edexcel International A Level
- Subject: WST01 Statistics 1 (S1) (https://mathvsarham.com/past-papers/wst01/)
- Session: January 2023
- Paper: 01
- Component code: WST01/01
- Time allowed: 90 minutes
- Total marks: 75
- Pages: 24

## Question paper text

Extracted automatically from the PDF; diagrams are missing and notation may be imperfect.

Question 1
The histogram shows the times taken, t minutes, by each of 100 people to swim 500 metres.
[Diagram or table: see page 2 of the paper]
(a) Use the histogram to complete the frequency table for the times taken by the 100 people to swim 500 metres.
[Diagram or table: see page 2 of the paper]
[1]
(b) Estimate the number of people who took less than 16 minutes to swim 500 metres. [2]
(c) Find an estimate for the mean time taken to swim 500 metres. [2]
Given that ft^2 = 41 033 ∑
(d) find an estimate for the standard deviation of the times taken to swim 500 metres. [2]
Given that Q_3 = 23
(e) use linear interpolation to estimate the interquartile range of the times taken to swim 500 metres. [3]

Question 2
Two bags, X and Y, each contain green marbles (G) and blue marbles (B) only.
• Bag X contains 5 green marbles and 4 blue marbles
• Bag Y contains 6 green marbles and 5 blue marbles
A marble is selected at random from bag X and placed in bag Y A second marble is selected at random from bag X and placed in bag Y A third marble is then selected, this time from bag Y
(a) Use this information to complete the tree diagram shown on page 7 [3]
(b) Find the probability that the 2 marbles selected from bag X are of different colours. [2]
(c) Find the probability that all 3 marbles selected are the same colour. [2]
Given that all three marbles selected are the same colour,
(d) find the probability that they are all green. [3]
[Diagram or table: see page 7 of the paper]
Answer: ____
[Diagram or table: see page 7 of the paper]
Answer: ____
[Diagram or table: see page 7 of the paper]
Answer: ____
[Diagram or table: see page 7 of the paper]
Answer: ____
Answer: ____
[Diagram or table: see page 7 of the paper]
Answer: ____
9
Answer: ____
[Diagram or table: see page 7 of the paper]
Answer: ____
[Diagram or table: see page 7 of the paper]

Question 3
The probability distribution of the discrete random variable X is given by
[Diagram or table: see page 10 of the paper]
where a is a constant.
(a) Find, in terms of a, E(X) [2]
(b) Find the range of the possible values of E(X) [3]
Given that Var(X) = 0.56
(c) find the possible values of a [6]

Question 4
(i) In the Venn diagram below, A and B represent events and p, q, r and s are probabilities.
[Diagram or table: see page 12 of the paper]
(a) Use algebra to show that 2p + 2q + 2r = 4/5 [4]
(b) Find the value of p, the value of q, the value of r and the value of s [5]
(ii) Two events, C and D, are such that
[Diagram or table: see page 12 of the paper]
where x is a positive constant.
By considering P(C) + P(D) show that C and D cannot be mutually exclusive. [4]

Question 5
The lengths, L mm, of housefly wings are normally distributed with L ~ N(4.5, 0.4^2)
(a) Find the probability that a randomly selected housefly has a wing length of less than 3.86 mm. [3]
(b) Find
(i) the upper quartile (Q_3) of L
(ii) the lower quartile (Q_1) of L [4]
A value that is greater than Q_3+ 1.5 × (Q_3– Q_1) or smaller than Q_1– 1.5 × (Q_3– Q_1) is defined as an outlier.
(c) Find these two outlier limits. [3]
A housefly is selected at random.
(d) Using standardisation, show that the probability that this housefly is not an outlier is 0.993 to 3 decimal places. [3]
Given that this housefly is not an outlier,
(e) showing your working, find the probability that the wing length of this housefly is greater than 5 mm. [4]

Question 6
A research student is investigating the maximum weight, y grams, of sugar that will dissolve in 100 grams of water at various temperatures, x °C, where 10  x  80
The research student calculated the regression line of y on x and found it to be
[Diagram or table: see page 20 of the paper]
(a) Give an interpretation of the gradient of the regression line. [1]
(b) Use the regression line to estimate the maximum weight of sugar that will dissolve in 100 grams of water when the temperature is 90 °C. [2]
(c) Comment on the reliability of your estimate, giving a reason for your answer. [2]
Using the regression line of y on x and the following summary statistics
[Diagram or table: see page 20 of the paper]
(d) show that the product moment correlation coefficient for these data is 0.988 to 3 decimal places. [7]
The research student’s supervisor plotted the original data on a scatter diagram, shown on page 23
With reference to both the scatter diagram and the correlation coefficient,
(e) discuss the suitability of a linear regression model to describe the relationship between x and y. [2]
[Diagram or table: see page 23 of the paper]