# WST01 Statistics 1 (S1) May/June 2021 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wst01/2021-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wst01/WST01_may-june_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: May/June 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
There are 7 red counters, 3 blue counters and 2 yellow counters in a bag. Gina selects a counter at random from the bag and keeps it. If the counter is yellow she does not select any more counters. If the counter is not yellow she randomly selects a second counter from the bag.
(a) Complete the tree diagram.
[Diagram or table: see page 2 of the paper]
[2]
Given that Gina has selected a yellow counter,
(b) find the probability that she has 2 counters. [3]

Question 2
In the Venn diagram below, A, B and C are events and p, q, r and s are probabilities.
The events A and C are independent and P(A) = 0.65
[Diagram or table: see page 4 of the paper]
(a) State which two of the events A, B and C are mutually exclusive. [1]
(b) Find the value of r and the value of s. [5]
The events (A ∩ C′) and (B ∪ C) are also independent.
(c) Find the exact value of p and the exact value of q. Give your answers as fractions. [6]

Question 3
A random sample of 100 carrots is taken from a farm and their lengths, L cm, recorded. The data are summarised in the following table.
[Diagram or table: see page 6 of the paper]
A histogram is drawn to represent these data. The bar representing the class 5  L < 8 is 1.5 cm wide and 1 cm high.
(a) Find the width and height of the bar representing the class 15  L < 20 [3]
(b) Use linear interpolation to estimate the median length of these carrots. [2]
(c) Estimate
(i) the mean length of these carrots, [2]
(ii) the standard deviation of the lengths of these carrots. [3]
A supermarket will only buy carrots with length between 9 cm and 22 cm.
(d) Estimate the proportion of carrots from the farm that the supermarket will buy. [2]
Any carrots that the supermarket does not buy are sold as animal feed.
The farm makes a profit of 2.2 pence on each carrot sold to the supermarket, a profit of 0.8 pence on each carrot longer than 22 cm and a loss of 1.2 pence on each carrot shorter than 9 cm.
(e) Find an estimate of the mean profit per carrot made by the farm. [2]

Question 4
Kris works in the mailroom of a large company and is responsible for all the letters sent by the company. The weights of letters sent by the company, W grams, have a normal distribution with mean 165 g and standard deviation 35 g.
(a) Estimate the proportion of letters sent by the company that weigh less than 120 g. [3]
Kris splits the letters to be sent into 3 categories: heavy, medium and light, with 1/3 of the letters in each category.
(b) Find the weight limits that determine medium letters. [4]
A heavy letter is chosen at random.
(c) Find the probability that this letter weighs less than 200 g. [3]
Kris chooses a random sample of 3 letters from those in the mailroom one day.
(d) Find the probability that there is one letter in each of the 3 categories. [3]

Question 5
The discrete random variable X has the following probability distribution
[Diagram or table: see page 14 of the paper]
Given that E(X ) = 0.5
(a) find the value of a. [2]
Given also that Var(X ) = 5.01
(b) find the value of b and the value of c. [5]
The random variable Y = 5 − 8X
(c) Find (i) E(Y )
(ii) Var(Y ) [3]
(d) Find P(4X^2 > Y) [5]

Question 6
Two economics students, Andi and Behrouz, are studying some data relating to unemployment, x%, and increase in wages, y%, for a European country. The least squares regression line of y on x has equation
[Diagram or table: see page 18 of the paper]
(a) Show that S_yy = 7.524 375 [1]
(b) Find S_xx [4]
(c) Find the product moment correlation coefficient between x and y. [3]
Behrouz claims that, assuming the model is valid, the data show that when unemployment is 2% wages increase at over 3%
(d) Explain how Behrouz could have come to this conclusion. [1]
Andi uses the formula
[Diagram or table: see page 18 of the paper]
to estimate the range of values for x.
(e) Find estimates of the minimum value and the maximum value of x in these data using Andi’s formula. [3]
(f) Comment, giving a reason, on the reliability of Behrouz’s claim. [2]
Andi suggests using the regression line with equation y = 3.684 – 0.3242x to estimate unemployment when wages are increasing at 2%
(g) Comment, giving a reason, on Andi’s suggestion. [2]
[Diagram or table: see page 20 of the paper]