Find the total frequency.

Total frequency is the sum of all frequencies:

The frequency for $60 < s \le 64$ is 6.
The frequency for $64 < s \le 70$ is 12.
So, the frequency for $60 < s \le 70$ is $6 + 12 = 18$.

The sector angle is calculated as $\frac{\text{frequency for the group}}{\text{total frequency}} \times 360^\circ$.

The sector angle for the speed $60 < s \le 70$ is $\boxed{\text{129.6}^\circ}$.

Frequencies for $40 < s \le 50$, $50 < s \le 60$, and $60 < s \le 64$ are 3, 14, and 6 respectively.
Sum $= 3 + 14 + 6 = 23$.

The interval $64 < s \le 70$ has a frequency of 12 cars over a range of $70 - 64 = 6 \text{ km/h}$.
We need to estimate for the range $64 < s \le 68$, which is $68 - 64 = 4 \text{ km/h}$.
Estimated frequency for $64 < s \le 68 = \frac{4}{6} \times 12 = 8$.

Total estimated number of cars with speed less than $68 \text{ km/h} = 23 + 8 = 31$.
The estimated number of cars whose speed was less than $68 \text{ km/h}$ is $\boxed{\text{31}}$.

This corresponds to the interval $70 < s \le 80$, which has a frequency of 15.

This corresponds to the intervals $40 < s \le 50$ and $50 < s \le 60$.
Frequency $= 3 + 14 = 17$.

Total frequency $= 50$.

Let A be the event that a car has speed $> 70 \text{ km/h}$. $P(A) = \frac{15}{50}$.
Let B be the event that a car has speed $\le 60 \text{ km/h}$. $P(B) = \frac{17}{50}$.
When two cars are chosen at random, the probability that one car had speed $> 70 \text{ km/h}$ AND the other had speed $\le 60 \text{ km/h}$ is given by:
$P(\text{one A and one B}) = P(A \text{ then } B) + P(B \text{ then } A)$
Since cars are chosen without replacement:
$P(A \text{ then } B) = \frac{15}{50} \times \frac{17}{49}$
$P(B \text{ then } A) = \frac{17}{50} \times \frac{15}{49}$
So, the total probability is:

The probability is $\boxed{\frac{51}{245}}$.

• $40 < s \le 50$: Midpoint $= \frac{40+50}{2} = 45$
• $50 < s \le 60$: Midpoint $= \frac{50+60}{2} = 55$
• $60 < s \le 64$: Midpoint $= \frac{60+64}{2} = 62$
• $64 < s \le 70$: Midpoint $= \frac{64+70}{2} = 67$
• $70 < s \le 80$: Midpoint $= \frac{70+80}{2} = 75$

Sum $= (45 \times 3) + (55 \times 14) + (62 \times 6) + (67 \times 12) + (75 \times 15)$
Sum $= 135 + 770 + 372 + 804 + 1125$
Sum $= 3206$

Total frequency $= 50$ (from part a).

Mean speed $= \frac{\text{Sum of (midpoint } \times \text{ frequency)}}{\text{Total frequency}}$

The estimate of the mean speed is $\boxed{\text{64.12 km/h}}$.