Simulation DATA-SCIENCE-OPTIMIZE Practice Questions (Page 5)

Questions 21–21

1. 21application · medium

   A retail analyst is modeling the total daily sales for a store. Daily customer count follows a normal distribution with mean 200 and standard deviation 30, and each customer spends an amount that is uniformly distributed between $20 and $50. The analyst needs to estimate the probability that total daily sales exceed $6,000. Which approach best estimates this probability?

   • ASimulate only the customer count, assume each customer spends exactly $35, and count how often the count times $35 exceeds $6,000.
   • BCompute the expected total sales as 200 × $35 = $7,000 and conclude the probability is high because the mean exceeds $6,000.
   • CUse the central limit theorem to approximate the total as normal with mean $7,000 and standard deviation $35, then find the z-score for $6,000.
   • DRun a Monte Carlo simulation: for each iteration, draw a customer count from the normal distribution, then draw that many spending amounts from the uniform distribution, sum them, and record the total. Repeat many times and compute the proportion of totals above $6,000.
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