The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200 minutes, with the results shown in the table below. Complete (a) through (c) to the right. \begin{tabular}{cc} Arrivals & Frequency \\ \hline 0 & 21 \\ 1 & 35 \\ 2 & 40 \\ 3 & 36 \\ 4 & 28 \\ 5 & 22 \\ 6 & 11 \\ 7 & 5 \\ 8 & 2 \end{tabular} a. Compute the expected number of arrivals per minute. \[ \mu=\square \] (Type an integer or decimal rounded to three decimal places as needed.)

Step 1 ：Define the number of arrivals and their frequencies as follows: Arrivals = [0, 1, 2, 3, 4, 5, 6, 7, 8] and Frequencies = [21, 35, 40, 36, 28, 22, 11, 5, 2].

Step 2 ：Calculate the total number of arrivals by multiplying each arrival by its frequency and summing them all up. The total number of arrivals is \( \sum_{i=1}^{n} a_i \cdot f_i = 562 \), where \( a_i \) is the number of arrivals and \( f_i \) is the frequency.

Step 3 ：Calculate the total number of minutes by summing up all the frequencies. The total number of minutes is \( \sum_{i=1}^{n} f_i = 200 \).

Step 4 ：Calculate the expected number of arrivals per minute by dividing the total number of arrivals by the total number of minutes. The expected number of arrivals per minute is \( \frac{total\_arrivals}{total\_minutes} = 2.81 \).

Step 5 ：The expected number of arrivals per minute is \(\boxed{2.81}\).