# WST01 Statistics 1 (S1) May/June 2022 Paper 01

Pearson Edexcel International A Level WST01 Statistics 1 (S1) past paper 01, May/June 2022. Open it online or download the question paper PDF free.

- Page: https://mathvsarham.com/past-papers/wst01/2022-may-june-paper-01/
- PDF: https://mathvsarham.com/papers/wst01/WST01_may-june_2022_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 2022
- 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 company Seafield requires contractors to record the number of hours they work each week. A random sample of 38 weeks is taken and the number of hours worked per week by contractor Kiana is summarised in the stem and leaf diagram below.
[Diagram or table: see page 2 of the paper]
The quartiles for this distribution are summarised in the table below.
[Diagram or table: see page 2 of the paper]
(a) Find the values of w, x and y [3]
Kiana is looking for outliers in the data. She decides to classify as outliers any observations greater than
[Diagram or table: see page 2 of the paper]
(b) Showing your working clearly, identify any outliers that Kiana finds. [2]
(c) Draw a box plot for these data in the space provided on the grid opposite. [3]
(d) Use the formula
[Diagram or table: see page 2 of the paper]
to find the skewness of these data. Give your answer to 2 significant figures. [2]
Kiana’s new employer, Landacre, wishes to know the average number of hours per week she worked during her employment at Seafield to help calculate the cost of employing her.
(e) Explain why Landacre might prefer to know Kiana’s mean, rather than median, number of hours worked per week. [1]
[Diagram or table: see page 3 of the paper]
[Diagram or table: see page 5 of the paper]

Question 2
Stuart is investigating the relationship between Gross Domestic Product (GDP) and the size of the population for a particular country. He takes a random sample of 9 years and records the size of the population, t millions, and the GDP, g billion dollars for each of these years.
The data are summarised as
[Diagram or table: see page 6 of the paper]
(a) Calculate the product moment correlation coefficient between t and g [3]
(b) Give an interpretation of your product moment correlation coefficient. [1]
(c) Find the equation of the least squares regression line of g on t in the form g = a + bt [4]
(d) Give an interpretation of the value of b in your regression line. [1]
(e)(i) Use the regression line from part (c) to estimate the GDP, in billions of dollars, for a population of 7 000 000 [2]
(ii) Comment on the reliability of your answer in part (i). Give a reason, in context, for your answer. [1]
Using the regression line from part (c), Stuart estimates that for a population increase of x million there will be an increase of 0.1 billion dollars in GDP.
(f) Find the value of x [2]

Question 3
Gill buys a bag of logs to use in her stove. The lengths, l cm, of the 88 logs in the bag are summarised in the table below.
[Diagram or table: see page 10 of the paper]
A histogram is drawn to represent these data. The bar representing logs with length 27 < l  30 has a width of 1.5 cm and a height of 4 cm.
(a) Calculate the width and height of the bar representing log lengths of 20 < l  25 [3]
(b) Use linear interpolation to estimate the median of l [2]
The maximum length of log Gill can use in her stove is 26 cm. Gill estimates, using linear interpolation, that x logs from the bag will fit into her stove.
(c) Show that x = 62 [1]
Gill randomly selects 4 logs from the bag.
(d) Using x = 62 , find the probability that all 4 logs will fit into her stove. [2]
The weights, W grams, of the logs in the bag are coded using y = 0.5w – 255 and summarised by
[Diagram or table: see page 10 of the paper]
(e) Calculate
(i) the mean of W [3]
(ii) the variance of W [3]

Question 4
The events H and W are such that
[Diagram or table: see page 14 of the paper]
Given that H and W are independent,
(a) show that P(W ) = 3/5 [4]
The event N is such that
[Diagram or table: see page 14 of the paper]
(b) Find P(N ′½H ) [2]
Given that W and N are mutually exclusive,
(c) draw a Venn diagram to represent the events H, W and N giving the exact probabilities of each region in the Venn diagram. [5]

Question 5
A red spinner is designed so that the score R is given by the following probability distribution.
[Diagram or table: see page 18 of the paper]
(a) Show that E(R^2) = 15.8 [1]
Given also that E(R) = 3.7
(b) find the standard deviation of R, giving your answer to 2 decimal places. [2]
A yellow spinner is designed so that the score Y is given by the probability distribution in the table below. The cumulative distribution function F( y) is also given.
[Diagram or table: see page 18 of the paper]
(c) Write down the value of d [1]
Given that E(Y ) = 4.55
(d) find the value of c [5]
Pabel and Jessie play a game with these two spinners. Pabel uses the red spinner. Jessie uses the yellow spinner. They take turns to spin their spinner. The winner is the first person whose spinner lands on the number 2 and the game ends. Jessie spins her spinner first.
(e) Find the probability that Jessie wins on her second spin. [2]
(f) Calculate the probability that, in a game, the score on Pabel’s first spin is the same as the score on Jessie’s first spin. [3]

Question 6
A manufacturer fills bottles with oil. The volume of oil in a bottle, V ml, is normally distributed with V ~ N(100, 2.5^2)
(a) Find P(V > 104.9) [3]
(b) In a pack of 150 bottles, find the expected number of bottles containing more than 104.9 ml [2]
(c) Find the value of v, to 2 decimal places, such that P(V > v ½V < 104.9) = 0.2801 [6]
[Diagram or table: see page 24 of the paper]