Chapter 5 - Discrete Probability Distributions - 5-5 Poisson Probability Distributions - Basic Skills and Concepts - Page 234: 16

a)0.0875 b)0.0826

a)$P(X=18)=\frac{19.6^{18}\cdot e^{-19.6}}{18!}=0.0875.$ Expected number: $0.0875\cdot40=3.5.$ This is not very close to the actual value. b)$P(X=21)=\frac{19.6^{21}\cdot e^{-19.6}}{21!}=0.0826.$ Expected number: $0.0826\cdot40=3.3.$ This is very close to the actual value.