(Solved): 1 Modeling Interarrival Time This section is meant to show you the usefulness of Excel in deriving ...

1 Modeling Interarrival Time This section is meant to show you the usefulness of Excel in deriving the basic descriptive statistics for the interarrival time \( A \). To begin, notice there are two columns labeled "Arrivals (per minute)" and "Interarrival time (minutes)." The first column details \( n=500 \) samples of arrivals per minute during a particularly busy period for a department store. The second column will be used to measure the corresponding interarrival times. To begin the analysis, in cell B2, type "=IF \( (\mathrm{A} 2=0,0, \operatorname{ROUND}(1 / \mathrm{A} 2,2)) \) " and (using the fill box at the bottom of the cell) drag the formula down to cell B501. Note you can also simply double-click on the fill box in cell B2 and it will auto-fill down to B501. We now have a sample of \( n=500 \) values for the variable \( A \). 1. What is the distribution of \( A \) ? (Hint: in cell E1, type "=ROUND(AVERAGE(A2:A501),1)" to generate the mean arrival rate \( \lambda \).) Using this distribution, what are the descriptive statistics (mean and standard deviation) of the variable \( A \), in minutes? 2. We can check the above question by directly analyzing the \( n=500 \) samples via a few simple Excel formulas. To derive the mean, type " \( =\operatorname{ROUND}(\mathrm{AVERAGE}(\mathrm{B} 2: \mathrm{B} 501), 1) \) " in cell E2 and then "=ROUND(STDEV.S(B2:B501),1)" in cell E3 for the standard deviation. Comparing to the above statistics, what do you notice? 3. What is the probability the interarrival time will be less than 30 seconds ( \( 0.5 \) minutes) between customers?