Find the value of \( p \) and \( q \).

Total rolls = 16, so:

\[ p + q + 4 + 2 + 0 + 3 = 16 \]

\[ p + q + 9 = 16 \]

\[ p + q = 7 \quad (1) \]

Mean score = 3:

\[ \frac{(1 \cdot p) + (2 \cdot q) + (3 \cdot 4) + (4 \cdot 2) + (5 \cdot 0) + (6 \cdot 3)}{16} = 3 \]

\[ p + 2q + 12 + 8 + 0 + 18 = 48 \]

\[ p + 2q + 38 = 48 \]

\[ p + 2q = 10 \quad (2) \]

Subtract (1) from (2):

\[ (p + 2q) – (p + q) = 10 – 7 \]

\[ q = 3 \]

Substitute into (1):

\[ p + 3 = 7 \]

\[ p = 4 \]

Verify: Frequencies sum = \( 4 + 3 + 4 + 2 + 0 + 3 = 16 \).

Mean: \[ \frac{4 + 6 + 12 + 8 + 0 + 18}{16} = \frac{48}{16} = 3 \]

Answer: \( p = 4 \), \( q = 3 \)

Write down the mean final score.

Each score is multiplied by 10. Mean final score = original mean × 10:

\[ 3 \cdot 10 = 30 \]

Answer: 30