4.17 Poisson distributionIB Maths: Applications and Interpretation HL: Mind map

Exam questions on 4.17 Poisson distribution

1. Calls to a school office arrive independently at a uniform average rate of $4$ calls per hour. Let $N$ be the number of calls in a one-hour period.
   Find the probability that at least $2$ calls arrive in a $30$-minute period.2 marks
2. Flaws occur in rolls of fabric independently of each other, at a uniform average rate of $0.8$ per square metre in fabric X and $1.5$ per square metre in fabric Y.
   Two square metres of fabric X and one square metre of fabric Y are inspected. Use your GDC to find the probability that more than $3$ flaws are found in total.2 marks
3. Patients arrive at the emergency department of a hospital during the night at an average rate of $5$ per hour. Let $X$ be the number of patients who arrive in a one-hour period during the night.
   State two conditions needed for $X$ to be modelled by a Poisson distribution, and give one reason why arrivals at an emergency department might not satisfy a condition.3 marks