Question 6:
6 | Recovery within working is allowed, e.g. a notation error in the working where the following line of working makes the candidate’s intent clear.
PMT
9709/52 Cambridge International AS & A Level – Mark Scheme February/March 2023
PUBLISHED
Abbreviations
AEF/OE Any Equivalent Form (of answer is equally acceptable) / Or Equivalent
AG Answer Given on the question paper (so extra checking is needed to ensure that the detailed working leading to the result is valid)
CAO Correct Answer Only (emphasising that no ‘follow through’ from a previous error is allowed)
CWO Correct Working Only
ISW Ignore Subsequent Working
SOI Seen Or Implied
SC Special Case (detailing the mark to be given for a specific wrong solution, or a case where some standard marking practice is to be varied in the
light of a particular circumstance)
WWW Without Wrong Working
AWRT Answer Which Rounds To
© UCLES 2023 Page 5 of 15
Question | Answer | Marks | Guidance
--- 6(a) ---
6(a) |  74−62.3
[P(X < 74) =] PZ     =P ( Z 1.393 ) 
 8.4  | M1 | Use of ± standardisation formula with 74, 62.3 and 8.4
substituted appropriately, not 8.42, not √8.4, no continuity
correction.
= 0.918 | A1 | 0.918 ⩽ p ⩽ 0.9185 .
2
Question | Answer | Marks | Guidance
--- 6(b) ---
6(b) | 50−62.3 74−62.3
[P ( 50 X 74 ) = P] Z  
 8.4 8.4 
[P(−1.464Z 1.393)] | M1 | Use of ± standardisation formula with both 74 (may be seen in
6(a) if their value seen) & 50, 62.3 and 8.4 substituted
appropriately.
Condone use of 8.42, 8.4 and continuity correction ±0.5
(73.5 or 74.5 and 49.5 or 50.5).
( )+Φ ( )−1
[Φ 1.464 1.393 ]
0.9285 + 0.9182 – 1 | M1 | Calculating the appropriate probability area from stated Φ of
z-values (leading to their final answer > 0.5) but not
symmetrical values.
= 0.847 | A1 | 0.8465 ⩽ p < 0.8475 .
SC B1 for 0.8465 ⩽ p < 0.8475 if M0A0 awarded.
( 0.8467 )4 =0.514 | B1 FT | Accept 0.513 ⩽ p ⩽ 0.514 .
FT (their 4-figure p)4, 0 < p < 1.
4
--- 6(c) ---
6(c) | 36−
z = =−0.739
1 
54−
z = =1.282
2  | B1 | −0.740 < z < −0.738 or 0.738 < z < 0.740 .
1 1
B1 | z = ±1.282 (critical value).
2
M1 | Use of the ±standardisation formula once with μ, σ and a z-
value (not 0.23, 0.77, 0.90, 0.10, ±0.261, ±0.282…). Condone
continuity correction ±0.5, not 2, .
Solve, obtaining values for  and σ
=42.6,  =8.91 | M1 | Solve using the elimination method, substitution method or
other appropriate approach to obtain values for both μ and σ.
A1 | 42.58 ⩽ µ ⩽ 42.6,
8.90 ⩽ σ ⩽ 8.91 .
5
Question | Answer | Marks | Guidance