Download Statistics and Modelling: Use probability distribution models to solve

Assessment Schedule
Statistics and Modelling: Use probability distribution models to solve straightforward problems (90646)
Achievement
Use probability distribution
models to solve straightforward
problems.
Q
a
b
Normal distribution (µ = 192, σ
= 28):
P(X > 180)
=
P(Z > - 0.429) = 0.666 (G.C.
Normal distribution (µ = ?, σ =
0.6):
P(X > 133) < 0.01
z = 2.33
Achievement with Merit
Use probability distribution
models to solve problems.
Achievement with Excellence
Use and justify probability
distribution models to solve
complex problems.
Judgement
Accept CAO without any
working.
A: 1a or 1b
M: 1b
133  
 2.33
0.6
Re-arranging to solve gives:
µ = 131.6 grams
Accept µ consistent with
z score which may vary
with rounding,
Answer should be
rounded to at least 4 sig.
fig.
1
Ignore units
c
Sufficiency
Award a single grade for
each question holistically
in reference to the
achievement criteria
Poisson distribution (λ = ?):
P(X ≥ 1) = 0.26
P(X = 0) = 0.74
e-λ = 0.74
λ = 0.301
So the mean number of declined
credit card transactions per hour
is 0.301.
Accept λ consistent with
with rounding
E: 1c
Achievement
Use probability distribution
models to solve
straightforward problems.
Q
a
b
c
2
Binomial distribution (n = 20,
p = 0.1):
P(X ≥ 2) = 0.608 (G.C.)
Binomial distribution (n = 10,
p = 0.25):
P(X ≤ 5) = 0.980 (G.C.)
Binomial distribution (n = 10,
p = 0.2):
P(X ≤ 5) = 0.994 (G.C.)
Achievement with Merit
Use probability distribution
models to solve problems.
Achievement with Excellence
Use and justify probability
distribution models to solve
complex problems.
Judgement
Accept CAO without any
working.
P(no more than half black and
no more than half white
zPhones are faulty) = 0.980 x
0.994 = 0.974
Accept CAO without any
working.
Sufficiency
Award a single grade for
each question holistically
in reference to the
achievement criteria
A: 2a or 2b
M: 2b
E: 2c
Select distribution:
X can be modelled by Poisson
distribution
Justify:
Two required
Occurrence of complaints
occurs randomly
Each complaint is independent
Complaints cannot occur
simultaneously
The probability of a complaint is
proportional to the length of the
time interval
Parameter(s):
For this data, λ is estimated to
be 1.25, as the mean number of
complaints per month is
estimated to be 1.25.
Distribution must be
selected, justified in
context and defined in
reference to its
parameter(s)
Or equivalent for λ
Achievement
Use probability distribution
models to solve
straightforward problems.
Q
a
b
Achievement with Merit
Use probability distribution
models to solve problems.
Achievement with Excellence
Use and justify probability
distribution models to solve
complex problems.
Poisson distribution (λ = 3):
P(X ≤ 1) = 0.199 (G.C.)
Poisson distribution (λ = 3):
P(X = 0) = 0.05 (G.C.)
Judgement
Accept CAO without any
working.
Binomial distribution (n = 5, p =
0.05):
P(X = 2) = 0.021 (G.C.)
c
Accept CAO without any
working.
µT = 6 x 192 + 4 x 285
= 2292 seconds
= 38 minutes 12 seconds
σT = 6  282  4  422
= 108.4 seconds
= 1 minute 48.4 seconds
Or equivalent
Or equivalent
 P(X < 2300) =
P(Z < 0.074) = 0.529 (G.C.)
Overall
grade
A: 3a or 3b
M: 3b
E: 3c
Normal distribution:
3
Sufficiency
Award a single grade for
each question holistically
in reference to the
achievement criteria
Achievement
Achievement with Merit
Achievement with Excellence
Use probability distribution models to
solve straightforward problems.
Use probability distribution models to
solve problems.
Use and justify probability distribution
models to solve complex problems.
At least two questions graded A (or
higher)
Two questions graded M (or higher)
Two questions graded E