IB Mathematics Applications & Interpretation Question Type 1: Choosing the Correct Distribution for a Given Context Exercises

If the acceptance probability is increased to $0.30$ and you observe $8$ calls, what is the probability exactly $3$ are accepted?

Assuming the time between call arrivals is exponentially distributed with mean 3 minutes, what is the probability that you wait more than 5 minutes for the next call?

Given calls arrive as a Poisson process at 20 calls per hour and each is independently accepted with probability $0.25$, show the distribution of accepted calls in one hour and compute its mean.

A call center handles 200 calls with acceptance probability $0.05$. Use a Poisson approximation to find the probability it accepts at least 8 calls.

What is the probability that the 5th accepted call occurs on the 20th call attempt, with acceptance probability $0.25$?

Identify the probability distribution for the number of calls a call center receives in a 2-hour period, given that it receives on average one call every 3 minutes. State the parameter(s) of the distribution.

Calls arrive as a Poisson process with mean 100 per hour. Use the normal approximation to estimate $P(90\le X\le 110)$, where $X$ is the number of calls in one hour.

What is the probability there are no accepted calls in the next 15 minutes, given arrivals are Poisson at 5 per hour and each is accepted with probability $0.25$?

Find the probability that the first accepted call occurs on the 3rd call attempt, given that the probability of acceptance is $0.25$ for each independent call.

For 50 independent calls with acceptance probability $0.25$, state the distribution of the number of accepted calls and compute its mean and variance.

Calls follow a Poisson process at a rate of 5 per hour. What is the probability that the time until the $3^{\text{rd}}$ call is less than 30 minutes?

A call center accepts each call independently with probability $0.25$. What is the probability it accepts exactly $4$ calls out of $10$?