# WST01 Statistics 1 (S1) January 2021 Paper 01

Pearson Edexcel International A Level WST01 Statistics 1 (S1) past paper 01, January 2021. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wst01/2021-january-paper-01/
- PDF: https://mathvsarham.com/papers/wst01/WST01_january_2021_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 2021
- Paper: 01
- Component code: WST01/01
- Time allowed: 90 minutes
- Total marks: 75
- Pages: 20

## Question paper text

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

Question 1
The Venn diagram shows the events A, B and C and their associated probabilities.
[Diagram or table: see page 2 of the paper]
(a) P(Bʹ) [1]
(b) P(A ∪ C) [2]
(c) P(A | Bʹ ) [2]

Question 2
The stem and leaf diagram below shows the ages (in years) of the residents in a care home.
[Diagram or table: see page 4 of the paper]
(a) Find the median age of the residents. [1]
(b) Find the interquartile range (IQR) of the ages of the residents. [2]
An outlier is defined as a value that is either
more than 1.5 ´ (IQR) below the lower quartile or
more than 1.5 ´ (IQR) above the upper quartile.
(c) Determine any outliers in these data. Show clearly any calculations that you use. [3]
(d) On the grid on page 5, draw a box plot to summarise these data. [3]
[Diagram or table: see page 5 of the paper]

Question 3
The weights of packages that arrive at a factory are normally distributed with a mean of 18 kg and a standard deviation of 5.4 kg
(a) Find the probability that a randomly selected package weighs less than 10 kg [3]
The heaviest 15% of packages are moved around the factory by Jemima using a forklift truck.
(b) Find the weight, in kg, of the lightest of these packages that Jemima will move. [3]
One of the packages not moved by Jemima is selected at random.
(c) Find the probability that it weighs more than 18 kg [4]
A delivery of 4 packages is made to the factory. The weights of the packages are independent.
(d) Find the probability that exactly 2 of them will be moved by Jemima. [3]

Question 4
A spinner can land on the numbers 10, 12, 14 and 16 only and the probability of the spinner landing on each number is the same. The random variable X represents the number that the spinner lands on when it is spun once.
(a) State the name of the probability distribution of X. [1]
(b)(i) Write down the value of E(X ) [1]
(ii) Find Var(X ) [2]
A second spinner can land on the numbers 1, 2, 3, 4 and 5 only. The random variable Y represents the number that this spinner lands on when it is spun once. The probability distribution of Y is given in the table below
[Diagram or table: see page 10 of the paper]
(c) Find (i) E(Y ) [2]
(ii) Var(Y ) [3]
The random variable W = aX + b, where a and b are constants and a > 0 Given that E(W ) = E(Y ) and Var(W ) = Var(Y )
(d) find the value of a and the value of b. [5]
Each of the two spinners is spun once.
(e) Find P(W = Y ) [2]

Question 5
A company director wants to introduce a performance-related pay structure for her managers. A random sample of 15 managers is taken and the annual salary, y in £1000, was recorded for each manager. The director then calculated a performance score, x, for each of these managers. The results are shown on the scatter diagram in Figure 1 on the next page.
(a) Describe the correlation between performance score and annual salary. [1]
The results are also summarised in the following statistics.
[Diagram or table: see page 14 of the paper]
(b)(i) Show that S_xy = 2006 [1]
(ii) Find S_yy [2]
(c) Find the product moment correlation coefficient between performance score and annual salary. [2]
The director believes that there is a linear relationship between performance score and annual salary.
(d) State, giving a reason, whether or not these data are consistent with the director’s belief. [1]
(e) Calculate the equation of the regression line of y on x, in the form y = a + bx Give the value of a and the value of b to 3 significant figures. [4]
(f) Give an interpretation of the value of b. [1]
(g) Plot your regression line on the scatter diagram in Figure 1 [2]
The director hears that one of the managers in the sample seems to be underperforming.
(h) On the scatter diagram, circle the point that best identifies this manager. [1]
The director decides to use this regression line for the new performance related pay structure.
(i) Estimate, to 3 significant figures, the new salary of a manager with a performance score of 30 [2]
[Diagram or table: see page 15 of the paper]
Turn over for a spare copy of the scatter diagram if you need to redraw your line.
[Diagram or table: see page 17 of the paper]

Question 6
A disc of radius 1 cm is rolled onto a horizontal grid of rectangles so that the disc is equally likely to land anywhere on the grid. Each rectangle is 5 cm long and 3 cm wide. There are no gaps between the rectangles and the grid is sufficiently large so that no discs roll off the grid.
If the disc lands inside a rectangle without covering any part of the edges of the rectangle then a prize is won.
By considering the possible positions for the centre of the disc,
(a) show that the probability of winning a prize on any particular roll is 1/5 [3]
A group of 15 students each roll the disc onto the grid twenty times and record the number of times, x, that each student wins a prize. Their results are summarised as follows
[Diagram or table: see page 18 of the paper]
(b) Find the standard deviation of the number of prizes won per student. [2]
A second group of 12 students each roll the disc onto the grid twenty times and the mean number of prizes won per student is 3.5 with a standard deviation of 2
(c) Find the mean and standard deviation of the number of prizes won per student for the whole group of 27 students. [7]
The 27 students also recorded the number of times that the disc covered a corner of a rectangle and estimated the probability to be 0.2216 (to 4 decimal places).
(d) Explain how this probability could be used to find an estimate for the value of π and state the value of your estimate. [3]
[Diagram or table: see page 20 of the paper]