Mathematics · Oct / Nov 2024 · Paper 61 · Question 8
YMA01
As printed in the paper
The question as text
8. An orchard produces apples. The weights, A grams, of its apples are normally distributed with mean μ grams and standard deviation σ grams. It is known that P(A < 162) = 0.1 and P(162 < A < 175) = 0.7508
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8(a)[5]
or 175
−
μ
1.04
(Calculator gives 1.03987…)
=
μ
−
1.2816
=
162
μ
+
1.04
=
175
2.3216
13
=
=
5.5995...
awrt 5.6
μ=
169.1764...
awrt 169
8(b)[5]
Q =
208.26
or
Q
−
Q
=
13.48
1
3
1
221.74 1.5(221.74
+
−
'
')[ 241.96]
=
or
'
' 1.5(221.74
−
−
'
')[ 188.04]
=
Q
Q
Q
1
1
1
Probability of an outlier
1 – Probability of not an outlier
P
(
'241.96'
)
B
>
=
'241.96' 215
−
[
]
P
>
=
P(
>
2.70)
Z
Z
(
)
10
P '188.04'
<
<
'241.96'
=
B
or
'188.04' 215
−
'241.96' 215
−
(
)
P
<
Z
<
P
B
<
'188.04'
=
10
10
'188.04' 215
−
[
]
[
]
=
P( 2.70)
−
<
<
P(2.70)
P
<
=
P(
<−
2.70)
Z
Z
Z
10
or
=
0.0035
(Calculator gives 0.0034883…)
= 0.993 (Calculator gives 0.99298…)
P(Outlier)
2 '0.0035'
P(Outlier)
1 '0.993'
= ×
= −
=
0.007
(Calculator gives 0.006976…)
= 0.007 (Calculator gives 0.007017…)
awrt 0.007
awrt 0.007
Notes
For standardising with μand and setting = to a z value with
z >
1
(a)
M1
A1
For one correct equation in any form with correct z value as given or better
A1
For a 2nd correct equation in any form allow 2dp or better for the z value
Dependent on previous M1. For solving their 2 linear simultaneous equations (Can be implied by
dM1
both correct answers) If answers are incorrect then we need to see evidence of correct working
μ=
awrt169
=
awrt 5.6
A1
For
and
For
Q =
208.26
or
−
=
13.48
Do not accept rounded values
(b)
B1
Q
Q
1
3
1
For a correct method for finding 1 outlier limit, ft their
Q or their IQR. You will need to check
M1
1
that these are correct if no working shown.
Dependent on previous M1. For standardising using their limit(s), 215 and 10 (allow ±) May be
dM1
implied by ± awrt 2.70 or awrt 0.0035 or awrt 0.993 or final answer of awrt 0.007
If using the LHS of the MS: for multiplying their probability by 2
or
M1
If using the RHS of the MS: for 1 – their probability
May be implied by awrt 0.007
A1
awrt 0.007
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