A) Let $\displaystyle T_i$ be the random variable

*time between sale of ticket i-1 and ticket i*.

Then the pdf of $\displaystyle T_i$ is $\displaystyle f(t_i) = \frac{t_i^2 e^{-t_i/2}}{16}$ for $\displaystyle t_i \geq 0$ and zero elsewhere.

You require

$\displaystyle \Pr(T_1 + + T_2 + \, .... \, + T_{10} \leq 60) = \Pr(10T \leq 60)$

....Surely you jest, Mr. F.
since the $\displaystyle T_i$ are i.i.d. random variables

$\displaystyle = \Pr(T \leq 6) = \frac{1}{16} \int_0^6 t^2 \, e^{-t/2} \, dt$.

B) I suggest applying the Central Limit Theorem. n = 10 is too small to justify applying it.