Date | November 2020 | Marks available | 2 | Reference code | 20N.2.SL.TZ0.S_9 |
Level | Standard Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Calculate | Question number | S_9 | Adapted from | N/A |
Question
Fiona walks from her house to a bus stop where she gets a bus to school. Her time, W minutes, to walk to the bus stop is normally distributed with W~N(12, 32).
Fiona always leaves her house at 07:15. The first bus that she can get departs at 07:30.
The length of time, B minutes, of the bus journey to Fiona’s school is normally distributed with B~N(50, σ2). The probability that the bus journey takes less than 60 minutes is 0.941.
If Fiona misses the first bus, there is a second bus which departs at 07:45. She must arrive at school by 08:30 to be on time. Fiona will not arrive on time if she misses both buses. The variables W and B are independent.
Find the probability that it will take Fiona between 15 minutes and 30 minutes to walk to the bus stop.
Find σ.
Find the probability that the bus journey takes less than 45 minutes.
Find the probability that Fiona will arrive on time.
This year, Fiona will go to school on 183 days.
Calculate the number of days Fiona is expected to arrive on time.
Markscheme
* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.
0.158655
P(15<W<30)=0.159 A2 N2
[2 marks]
finding standardized value for 60 (A1)
eg z=1.56322
correct substitution using their z-value (A1)
eg 60-50σ=1.56322, 60-501.56322=σ
6.39703
σ=6.40 A1 N3
[3 marks]
0.217221
P(B<45)=0.217 A2 N2
[2 marks]
valid attempt to find one possible way of being on time (do not penalize incorrect use of strict inequality signs) (M1)
eg and , and
correct calculation for (seen anywhere) (A1)
eg
correct calculation for (seen anywhere) (A1)
eg
correct working (A1)
eg
(on time) A1 N2
[5 marks]
recognizing binomial with (M1)
eg
( from )
A1 N2
[2 marks]