Higher June 2025 Paper 2R Q20
20 The histogram gives some information about the weights, in grams, of some books.
75 books weigh less than 100 grams.
A book is chosen at random.
Find an estimate for the probability that this book weighs between 400 grams and 600 grams.
(4)
| Scheme | Marks |
|---|---|
| (frequency density =) 75 ÷ 100 (= 0.75) or any one correct value marked on the FD axis or uses their own linear FD scale to find the area of at least one of the third, fourth or fifth bars OR eg 1 (large) box / 1 (large) square = 12.5 books oe or 5 (sml) squares = 2.5 books or 1 (sml) square / 1 box = 0.5 books | M1 |
| eg using frequency densities 75 + (“2.25” × 100) + (“1” × 250) + (“2.5” × 50) + (“0.25” × 200) (= 75 + 225 + 250 + 125 + 50 = 725) OR eg using a measure of scale (eg large squares) (6 + 18 + 20 + 10 + 4) × “12.5” (=725) oe OR eg total no. of large squares = 6 + 18 + 20 + 10 + 4 (=58) or total no. of sml squares = 150 + 450 + 500 + 250 + 100 (=1450) | M1 |
| eg using frequency densities (“1” × 50) + (“2.5” × 50) + (“0.25” × 100) (= 50 + 125 + 25 = 200) OR eg using a measure of scale (eg large squares) (4 + 10 + 2) × “12.5” (=200) oe OR eg no. of large squares = 4 + 10 + 2 (= 16) or no. of sml squares = 100 + 250 + 50 (= 400) | M1 |
Correct answer only scores full marks (unless from obviously incorrect working) Answer: \(\dfrac{200}{725}\) | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a correct calculation of frequency density
or a correct value on the frequency density axis
or use of their own linear frequency density scale to find the area of at least one of the third, fourth or fifth bars
OR
or a correct measure of scale
Implied by a correct frequency for the third (250), fourth (125) or fifth (50) bar
M1: for a method to work out the total number of books
OR the total number of squares
Allow one error in a frequency density value, class width value or number of squares but not an omission
Allow ft their own linear frequency density scale
M1: for a method to estimate the number of books between 400g and 600 g OR the total number of squares between 400 g and 600 g
Allow one error in a frequency density value, class width value or number of squares but not an omission
Allow ft their own linear frequency density scale
A1: oe eg \(\dfrac{8}{29}\) or any correct decimal or correct percentage rounded or truncated to 2sf. NB \(\dfrac{200}{725} = 0.27(58\ldots)\)
M3 for any complete method that relies only on counting squares,
eg counting large squares: \(\dfrac{4 + 10 + 2}{6 + 18 + 20 + 10 + 4}\)
Allow one error in number of squares in each of numerator and denominator but do not allow any omissions
Must use a consistent method for the award of more than one mark