A call center receives an average of $9$ calls per hour. What is the probability that in a randomly chosen hour, the center receives at most $4$ calls? Assume the number of calls follows a Poisson distribution.

In a certain city, it is found that $5\%$ of the drivers run red lights. If a traffic study observes $30$ drivers at an intersection, find the mean and standard deviation for the number of drivers expected to run red lights.

In a binomial experiment with n = 9 trials, how many ways can you have exactly 2 successes?

Customers arrive at a small coffee shop according to a Poisson distribution with a mean rate of $3$ customers per minute. The shop can serve a maximum of $3$ customers per minute at the counter. What is the probability that exactly $1$ customer is waiting after the first minute and that no customers are waiting after the second minute?

A consumer study found that $41\%$ of shoppers prefer buying organic groceries. Suppose $15$ shoppers are randomly selected. What is the probability that at least one of the selected shoppers prefers organic groceries?

A survey reports that $20\%$ of people who regret buying a certain car model say they made the purchase too late during the model's lifecycle. Suppose five such individuals are randomly selected.

Find the probability that either none or exactly one of the selected individuals says they bought the car too late.

A poll finds that $70\%$ of college students own a laptop. In a random sample of $12$ college students, what is the probability that between $5$ and $9$, inclusive, own a laptop?

During a study on $10$ students' habits, the number of students who study at least $2$ hours daily is recorded. Determine if $8$ students studying at least $2$ hours daily is significantly high using the range rule of thumb. Assume the probability of a student studying at least $2$ hours daily is $0.5$.

In a study about pet ownership, $300$ people were asked if they own a dog. The results are summarized below. Determine if this summary can be considered a probability distribution. Justify.

A fair coin is flipped $60$ times. What is the probability of getting at least $38$ heads? Justify the use of the normal approximation and estimate the $P$-value using the normal model.