Problems 3
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The document analyzes arrival data recorded over 200 minutes at a bank. It calculates: 1) The expected number of arrivals per day is 2.9. 2) The standard deviation is 1.772. 3) Using the formula for standard deviation, it sums the squared differences between each arrival frequency and the mean, multiplied by the corresponding probability.
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Problems 3
- 1. Problems 3: The number of arrivals per minute at a bank located in central business district of large city was recorded over a period of 200 minutes with the following results: Arrival Frequency 0 14 1 31 2 47 3 41 4 29 5 21 6 10 7 5 a. Compute the expected number of arrivals per day. b. Compute the standard deviation. Solution: Xi 0 1 2 3 4 5 6 7 8 fi 14 31 47 41 29 21 10 5 2 200 Fi/∑fi 14/200 31/200 47/200 41/200 29/200 21/200 10/200 5/200 2/200 P(Xi) 0.07 0.115 0.235 0.205 0.145 0.105 0.05 0.025 0.01 Standard deviation = = √3.14 = 1.772 (Xi x PXi) (0x0.07) (1x0.115) (2x0.235) (3x0.205) (4x0.145) (5x0.105) (6x0.05) (7x0.025) (8x0.01) 0 0.115 0.47 0.615 0.58 0.525 0.30 0.175 0.08 2.9 (Xi-µ)2 P(Xi) (0-2.9)2x(0.07) (1-2.9)2x(0.115) (2-2.9)2x(0.47) (3-2.9)2x(0.615) (4-2.9)2x(0.58) (5-2.9)2x(0.525) (6-2.9)2x(0.30) (7-2.9)2x(0.175) (8-2.9)2x(0.08) 0.588 0.559 0.190 0.002 0.175 0.463 0.480 0.420 0.260 3.14 8 2