Mathematics · Oct / Nov 2024 · Paper 61 · Question 4
YMA01
As printed in the paper
The question as text
4. In this question you must show all stages of your working. Solutions relying entirely on calculator technology are not acceptable. The distances, m miles, a motorbike travels on a full tank of petrol can be modelled by a normal distribution with mean 170 miles and standard deviation 16 miles.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
4(a)[2]
N(170,16 )
2
X
190 170
−
P
(
190
)
P
P
(
1.25
)
X
>
=
Z
>
=
Z
>
16
[
]
= −
1 0.8944
=
0.1056
awrt 0.106
(
)
P
>
=
0.9
4(b)[3]
X
d
170
or 170
d −
−
d
= −
1.2816
=
1.2816
(Calc value ±1.28155…)
16
16
d =
149.494...
awrt 149 dA1
Notes
NB correct answers with no working scores no marks
(a)
M1
For standardising using 190, 170 and 16 (May be implied by 1.25)
A1
awrt 0.106 Do not ISW
(b)
M1
For standardising and setting = z value, where 1 < |z| < 2
A1
A fully correct standardisation = a correct compatible z value to 4 dp or better.
dA1
Dependent on previous A1 149.5 or awrt 149
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