Suppose small aircraft arrive at a certain airport according to a Poisson process with rate $\alpha=8$ per hour, so that the number of arrivals during a time period of $t$ hours is a Poisson rv with parameter $\lambda=8t$.

• (a) What is the probability that exactly $5$ small aircraft arrive during a $1$-hour period? At least $5$? At least 10?
• (b) What are the expected value and standard deviation of the number of small aircraft that arrive during a $90$-min period?
• (c) What is the probability that at least $20$ small aircraft arrive during a $2\frac{1}{2}$-hour period? That at most $10$ arrive during this period?