Date | November 2020 | Marks available | 2 | Reference code | 20N.2.AHL.TZ0.H_5 |
Level | Additional Higher Level | Paper | Paper 2 | Time zone | Time zone 0 |
Command term | Find | Question number | H_5 | Adapted from | N/A |
Question
A survey of British holidaymakers found that 15 %15% of those surveyed took a holiday in the Lake District in 20192019.
A random sample of 1616 British holidaymakers was taken. The number of people in the sample who took a holiday in the Lake District in 20192019 can be modelled by a binomial distribution.
State two assumptions made in order for this model to be valid.
Find the probability that at least three people from the sample took a holiday in the Lake District in 20192019.
From a random sample of nn holidaymakers, the probability that at least one of them took a holiday in the Lake District in 20192019 is greater than 0.9990.999.
Determine the least possible value of nn.
Markscheme
people’s holidays are independent of each other R1
the proportion is constant (at 0.150.15) R1
[2 marks]
Χ~B(16, 0.15)X~B(16, 0.15)
P(Χ≥3)=0.439P(X≥3)=0.439 (M1)A1
[2 marks]
probability of at least one =1-=1− probability of none
⇒1-0.85n>0.999⇒1−0.85n>0.999 OR 0.85n<0.0010.85n<0.001 (A1)
attempt to solve inequality (M1)
n≥42.503…n≥42.503…
so least possible n=43n=43 A1
[3 marks]