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?