With 15% of tomatoes defective in batches of 20, the Poisson parameter $\lambda$ and $P(X=0)$ are:

1. The Poisson approximation to a binomial uses $\lambda=np$. 2. Here $\lambda=20\times 0.15=3$. 3. Then $P(x)=\dfrac{\lambda^{x}e^{-\lambda}}{x!}$, so $P(0)=\dfrac{3^{0}e^{-3}}{0!}=e^{-3}$. 4. $e^{-3}=0.0498$ to four decimal places. 5. $0.0388$ is the binomial value for $x=0$, not the Poisson one; $\lambda=0.15$ mistakes the proportion for the mean count. _Source: NECTA ACSEE 2023 Advanced Mathematics 142/2, Question 1: Probability_