# Question 6:

## Part (a):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $z = \pm\left(\frac{150 - 162}{7.5}\right)$ | M1 | For attempting to standardise with 150, 162 and 7.5; accept $\pm$; allow use of symmetry and therefore 174 instead of 150 |
| $z = -1.6$ | A1 | 1st A1 for $-1.6$ seen; allow 1.6 seen if 174 used or awrt 0.945 seen |
| $P(F > 150) = P(Z > -1.6) = 0.9452(0071...)$ awrt $\mathbf{0.945}$ | A1 | 2nd A1 for awrt 0.945; do not apply ISW if 0.9452 is followed by $1 - 0.9452$, award A0; correct answer only 3/3 |

## Part (b):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $z = \pm 0.2533$ (or better seen) | B1 | Giving $z = \pm 0.25$ or $\pm 0.253$ scores B0 but may get M1A1 |
| $(\pm)\frac{s - 162}{7.5} = 0.2533(47...)$ | M1 | For standardising with $s$, 162 and 7.5; allow $\pm$; only allow $0.24 \leq z \leq 0.26$ |
| $s = 163.9$ awrt $\mathbf{164}$ | A1 | Correct answer only scores B0M1A1 |

## Part (c):
| Answer/Working | Marks | Guidance |
|---|---|---|
| $z = \pm 1.2816$ (or better seen) | B1 | Allow awrt $\pm 1.28$ if B0 scored in (b) for $z =$ awrt $\pm 0.25$ |
| $\frac{162 - \mu}{9} = -1.2815515...$ | M1, A1 | M1 for attempting to standardise with 162, 9 and $\mu$; $1.26 < |z| < 1.31$; allow $\pm$; 1st A1 for correct equation with compatible signs |
| $\mu = 173.533...$ awrt $\mathbf{174}$ | A1 | 2nd A1 for awrt 174 (correct answer only scores B0M1A1A1); dependent on 1st A1. NB: $\frac{162-\mu}{9} = 1.2816 \Rightarrow \mu = 162 + 9 \times 1.2816 =$ awrt 174 gets A0A0 |