Math Problem Statement
The following is the distribution of the hourly number of trucks arriving at company’s warehouse. Trucks arriving per hour 0 1 2 3 4 5 6 7 8 frequency 52 151 130 102 45 12 5 1 2 Fit a Poisson distribution and test for goodness fit at the 5% level of significance.
Solution
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Math Problem Analysis
Mathematical Concepts
Statistics
Probability Theory
Poisson Distribution
Goodness-of-Fit Test
Chi-Square Test
Formulas
Poisson Probability Formula: P(X = k) = (λ^k * e^(-λ)) / k!
Mean of Observed Data: λ = Σ(x_i * f_i) / Σf_i
Chi-Square Statistic: χ² = Σ((O_i - E_i)² / E_i)
Theorems
Poisson Distribution
Chi-Square Goodness-of-Fit Test
Suitable Grade Level
Undergraduate Statistics / Advanced High School
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