# WST01 Statistics 1 (S1) Oct/Nov 2022 Paper 01

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

- Page: https://mathvsarham.com/past-papers/wst01/2022-oct-nov-paper-01/
- PDF: https://mathvsarham.com/papers/wst01/WST01_oct-nov_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: Oct/Nov 2022
- Paper: 01
- Component code: WST01/01
- Time allowed: 90 minutes
- Total marks: 75
- Pages: 28

## Question paper text

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

Question 1
The stem lengths of a sample of 120 tulips are recorded in the grouped frequency table below.
[Diagram or table: see page 2 of the paper]
A histogram is drawn to represent these data.
The area of the bar representing the 40  x 42 class is 16.5 cm
(a) Calculate the exact area of the bar representing the 42  x 45 class. [2]
The height of the tallest bar in the histogram is 10 cm.
(b) Find the exact height of the second tallest bar. [3]
Q_1 for these data is 45 cm.
(c) Use linear interpolation to find an estimate for
(i) Q_2
(ii) the interquartile range. [4]
One measure of skewness is given by
[Diagram or table: see page 2 of the paper]
(d) By calculating this measure, describe the skewness of these data. [2]

Question 2
The production cost, £c million, of a film and the total ticket sales, £t million, earned by the film are recorded for a sample of 40 films.
Some summary statistics are given below.
[Diagram or table: see page 6 of the paper]
(a) Find the exact value of S_tt and the exact value of S_ct [3]
(b) Calculate the value of the product moment correlation coefficient for these data. [2]
(c) Give an interpretation of your answer to part (b) [1]
(d) Show that the equation of the linear regression line of t on c can be written as
[Diagram or table: see page 6 of the paper]
where the values of the intercept and gradient are given to 3 significant figures. [3]
(e) Find the expected total ticket sales for a film with a production cost of £90 million. [2]
Using the regression line in part (d)
(f) find the range of values of the production cost of a film for which the total ticket sales are less than 80% of its production cost. [2]

Question 3
Morgan is investigating the body length, b centimetres, of squirrels.
A random sample of 8 squirrels is taken and the data for each squirrel is coded using
[Diagram or table: see page 10 of the paper]
The results for the coded data are summarised below
[Diagram or table: see page 10 of the paper]
(a) Find the mean of b [3]
(b) Find the standard deviation of b [3]
A 9th squirrel is added to the sample. Given that for all 9 squirrels x = 0
(c) find
(i) the body length of the 9th squirrel, [2]
(ii) the standard deviation of x for all 9 squirrels. [2]

Question 4
The cumulative distribution function of the discrete random variable W, which takes only the values 6, 7 and 8, is given by
[Diagram or table: see page 14 of the paper]
[4]

Question 5
The weights, W grams, of kiwi fruit grown on a farm are normally distributed with mean 80 grams and standard deviation 8 grams.
The table shows the classifications of the kiwi fruit by their weight, where k is a positive constant.
[Diagram or table: see page 16 of the paper]
One kiwi fruit is selected at random from those grown on the farm.
(a) Find the probability that this kiwi fruit is Large. [3]
35% of the kiwi fruit are Jumbo.
(b) Find the value of k to one decimal place. [4]
75% of Tiny kiwi fruit weigh more than y grams.
(c) Find the value of y giving your answer to one decimal place. [5]

Question 6
The Venn diagram shows the events A, B, C and D, where p, q, r and s are probabilities.
[Diagram or table: see page 20 of the paper]
(a) Write down the value of
(i) P(A)
(ii) P(A½B)
(iii) P(A½C ) [3]
(b) find the exact value of q and the exact value of r [6]
Given also that P(B ∪ C¢) = 5/8
(c) find the exact value of s [2]

Question 7
Adana selects one number at random from the distribution of X which has the following probability distribution.
[Diagram or table: see page 24 of the paper]
(a) Given that the number selected by Adana is not 5, write down the probability it is 0 [1]
(b) Show that E(X^2) = 75 [1]
(c) Find Var(X ) [3]
(d) Find Var(4 – 3X ) [2]
Bruno and Charlie each independently select one number at random from the distribution of X
(e) Find the probability that the number Bruno selects is greater than the number Charlie selects. [3]
Devika multiplies Bruno’s number by Charlie’s number to obtain a product, D
(f) Determine the probability distribution of D [4]
[Diagram or table: see page 28 of the paper]