Step 1 :First, we need to compute the expected number of arrivals per minute. This is done by multiplying each arrival number by its frequency, summing up these products, and then dividing by the total number of minutes. The total number of minutes is 200.
Step 2 :The sum of the products of arrivals and their frequencies is: \(0*21 + 1*35 + 2*4 + 3*36 + 4*28 + 5*22 + 6*11 + 7*5 + 8*2 = 0 + 35 + 8 + 108 + 112 + 110 + 66 + 35 + 16 = 490\)
Step 3 :So, the expected number of arrivals per minute is \(\frac{490}{200} = 2.45\)
Step 4 :Next, we need to compute the standard deviation. To do this, we first need to compute the variance. The variance is the average of the squared differences from the Mean.
Step 5 :The squared differences from the Mean are: \((0-2.45)^2*21 + (1-2.45)^2*35 + (2-2.45)^2*4 + (3-2.45)^2*36 + (4-2.45)^2*28 + (5-2.45)^2*22 + (6-2.45)^2*11 + (7-2.45)^2*5 + (8-2.45)^2*2\)
Step 6 :This simplifies to: \(5.0025*21 + 2.0025*35 + 0.2025*4 + 0.3025*36 + 2.4025*28 + 6.5025*22 + 12.6025*11 + 20.7025*5 + 30.8025*2 = 105.0525 + 70.0875 + 0.81 + 10.89 + 67.27 + 143.055 + 138.6275 + 103.5125 + 61.605 = 700.91\)
Step 7 :So, the variance is \(\frac{700.91}{200} = 3.50455\)
Step 8 :Finally, the standard deviation is the square root of the variance, which is \(\sqrt{3.50455} = 1.872\)
Step 9 :So, the expected number of arrivals per minute is \(\boxed{2.45}\) and the standard deviation is \(\boxed{1.872}\)