In a study on the effectiveness of different flu vaccines, four vaccines were tested with the following probabilities of preventing the flu:

Is this a probability distribution, and if so, what are its mean and standard deviation?

During a particular month, a hospital recorded a total of $120$ births. Assuming that births occur randomly and independently at a constant average rate, use the Poisson distribution to determine the probability that on a randomly selected day, exactly $3$ births occur. Assume that $1$ month is equal to $30$ days.

The graph shows the weights (in kilograms) of different fish caught during a fishing competition. Is the variable in the graph discrete or continuous? Explain your reasoning.

Based on a recent technology survey, $42\%$ of smartphone users enable two-factor authentication (2FA) for added security. For each of the following, assume that $15$ smartphone users are randomly selected. What is the probability that exactly $10$ of the selected users have enabled two-factor authentication?

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 factory machine produces light bulbs with a $90\%$ success rate. If a quality inspector checks $8$ bulbs, what is the probability that

(a) all $8$ bulbs are not defective?

(b) at most $5$ bulbs are not defective?

(c) more than $5$ bulbs are not defective?

A feeder gets on average 3.6 bird landings per hour. What is the probability exactly 3 birds land in one hour? Compute using the Poisson formula.

A traffic sensor records car arrivals every minute during the weekday morning rush hour. The arrival rate is much higher between 7:30–9:00 than at other times. Which Poisson condition is most likely violated if you try to model the entire 7:00–10:00 period as a single Poisson process, and what practical remedy should you apply?

On a TI-84, when using PoissonPDF(lambda, x) to compute P(X = x) for a Poisson distribution, what do the two inputs lambda and x represent?

A design team has $6$ engineers and $4$ designers. Two team members are chosen at random for a site visit. What is the probability that the pair contains one engineer and one designer?

Four cards are drawn at random without replacement from a standard $52$-card deck. What is the probability that all four cards are from the same suit?

A classroom has $40$ students, $6$ of whom are left-handed. Four students are chosen at random without replacement, and the number of left-handed students among the chosen four is recorded. Is this a binomial experiment? Select the best answer.