(Solved): 2) Suppose we roll a die 3600 times. Let Xi be the number showing on the ith roll. Let Sn=X ...

2) Suppose we roll a die 3600 times. Let $X_i$ be the number showing on the $i^{\text{th }}$ roll. Let $S_n=X_1+\dots X_n$. By the law of large number, we know that $S_n/n$ will be close to 3.5 . Approximate the probability that $S_n/n$ differs from 3.5 by more than 0.05 . Either write a numerical answer or leave it in terms of $?$ if you use normal approximation. 3) Let $X_1,\dots ,X_{100}$ be i.i.d. (independent and identically distributed) exponential random variable with parameter $?=1$. Approximate $\mathbb{P}\left({?}_{i=1}^{100}{X}_i>90\right).$ Your answer can be either numerical or in terms of $?$. 4) Suppose that the checkout time at the Art of Espresso has a mean of 5 minutes and a standard deviation of 2 minutes. Estimate the probability to serve at least 36 customers during a 3-hour and a half shift.