Time: 2 hours
A Level Edexcel Exam Set A Practice Paper 3
Do not write on this paper. Give your answers to 3 significant figures unless otherwise specified.
Section A: Statistics
1.
Sophia believes that the random variable B
be modelled by a discrete uniform distribution.
(a) Write down the probability distribution for B.
(b) Use this model to find the probability that someone is born in July, August, September
or October.
Sophia used data on the number of births per day in England and Wales from 2000 to 2015 and
found that the proportion of births that occurred in July, August, September or October was 0.383
(c) Co
t this information.
(d)
2.
(2)
(1)
(1)
(1)
Jordan is studying the daily total sunshine for Heathrow in 2015 using the large data set. The data
for one month are summarised below, with the daily total sunshine shown to the nearest hour.
0
1
2
3
4
5
6
7
8
9 10 11 12
Sunshine (hours)
2
4
5
2
0
2
2
2
3
2
3
1
2
Frequency
(a) Calculate the mean for these data, giving your answer to one decimal place.
(1)
(b) Calculate the standard deviation for these data, giving your answer to one decimal place.
(1)
The means and standard deviations of the daily total sunshine for the other months from the
large data set for Heathrow in 2015 are given below. The data are not in month order.
Month
A
B
C
D
E
6.12
3.04
4.33
6.10
6.57
Mean (hours)
4.42
3.13
3.63
3.37
4.44
Standard deviation (hours)
(c) Using your knowledge of the large data set, suggest, giving a reason, which month had
a mean of 3.04
(2)
The data for these months are summarised in the box plots below. They are not in month order or
the same order as in the table above.
V
W
X
Y
Z
0
2
A Level Edexcel Mathematics Set A Paper 3
4
6
8
10
Page 1 of 70
12
14
16
© ZigZag Education, 2019
(d)
3.
4.
(i)
(ii)
Which of the box plots has the greatest lower quartile?
Suggest, giving reasons, which of the months A E is most likely to be
summarised in box plot V.
(3)
At the end of 2001, Olga, a tree surgeon, realised that she had sustained a moderate or serious
injury at work during 48% of the years she had been working as a tree surgeon. At the
beginning of 2002, she started wearing more protective clothing at work to try to reduce the risk
of injury. For the next 14 years, she only sustained a moderate or serious injury during 3 years.
(a) Using a binomial distribution, investigate at the 5% level of significance whether there
after she started
wearing more protective clothing.
(b) State two assumptions regarding moderate and serious injuries that are necessary for the
distribution in part (a) to be valid. For each assumption, comment on whether it is
likely to be correct in context.
(4)
The table illustrates the contents of three bags.
Bag A
Bag B
Bag C
Blue
1
2
4
Yellow
2
3
5
Green
1
0
0
A counter is selected at random from each bag.
(a) Draw a tree diagram to represent this situation.
(b) Calculate the probability that three yellow counters are chosen, giving your answer as a
simplified fraction.
(c) Calculate the probability that more yellow than blue counters are chosen, giving your
answer as a simplified fraction.
(d) Given that at least one counter is yellow, calculate the probability that more yellow than
blue counters are chosen, giving your answer as a simplified fraction.
Jake and Mia are playing a game. Mia selects a random counter from bag A and places it in
bag B. She then selects a random counter from bag B and places it in bag C. Finally, she
selects a random counter from bag C. If the counter is green, Jake will pay her £5.
(e) The counter Mia selected from bag C was green. Comment on how likely it is that Mia
cheated. You must fully justify your answer.
5.
(6)
Alina is playing an arcade game where she chooses four characters who together fight a
monster. The lifespan, L minutes, of a character can be modelled by a normal distribution
with mean 12 minutes and standard deviation 3 minutes. For Alina to score 10 points, none
of the four characters must reach the end of their lifespan before 14 minutes passes.
(a) Find the probability that a randomly selected character will have a lifespan greater than
10 minutes.
At the start of a fight, Alina selects four new characters. Given that they have been fighting
the monster for 10 minutes and all four characters are still alive:
(b) find the probability that Alina will score 10 points.
Alina has two extra characters, so after the first 10 minutes of the fight, although none of her
characters has reached the end of their lifespan yet, she randomly selects two of the characters
in play and replaces them with the two new characters.
(c) Show that the probability that Alina will score 10 points is 0.113 to 3 significant figures.
After 6 months, Alina believes that she has improved at the game and the mean lifespan of the
characters is now more than 12 minutes. She takes a random sample of ten characters and
finds that their mean lifespan is 13.4 minutes.
(d)
at the 5% level of significance.
A Level Edexcel Mathematics Set A Paper 3
Page 2 of 70
(4)
(2)
(3)
(3)
(3)
(1)
(5)
(3)
(5)
© ZigZag Education, 2019