Date | November Example questions | Marks available | 2 | Reference code | EXN.2.SL.TZ0.8 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Find | Question number | 8 | Adapted from | N/A |
Question
The time, minutes, taken to complete a jigsaw puzzle can be modelled by a normal distribution with mean and standard deviation .
It is found that of times taken to complete the jigsaw puzzle are longer than minutes.
Use in the remainder of the question.
Six randomly chosen people complete the jigsaw puzzle.
By stating and solving an appropriate equation, show, correct to two decimal places, that .
Find the th percentile time to complete the jigsaw puzzle.
Find the probability that a randomly chosen person will take more than minutes to complete the jigsaw puzzle.
Find the probability that at least five of them will take more than minutes to complete the jigsaw puzzle.
Having spent minutes attempting the jigsaw puzzle, a randomly chosen person had not yet completed the puzzle.
Find the probability that this person will take more than minutes to complete the jigsaw puzzle.
Markscheme
* This sample question was produced by experienced DP mathematics senior examiners to aid teachers in preparing for external assessment in the new MAA course. There may be minor differences in formatting compared to formal exam papers.
(A1)
states a correct equation, for example, A1
attempts to solve their equation (M1)
A1
the solution to the equation is , correct to two decimal places AG
[4 marks]
let be the th percentile
attempts to use the inverse normal feature of a GDC to find (M1)
(mins) A1
[2 marks]
evidence of identifying the correct area under the normal curve (M1)
Note: Award M1 for a clearly labelled sketch.
A1
[2 marks]
let represent the number of people out of the six who take more than minutes to complete the jigsaw puzzle
(M1)
for example, or (A1)
A1
[3 marks]
recognizes that is required (M1)
Note: Award M1 for recognizing conditional probability.
(A1)
M1
A1
[4 marks]