A bank teller can serve up to $5$ customers per minute. The number of customers arriving each minute for $10$ minutes is: $4$, $6$, $5$, $7$, $3$, $8$, $5$, $2$, $6$, $7$. At the start, no customers are waiting. What is the number of customers waiting at the end of minute $10$?

A charity is selling $\mathrm{\backslash (}15$ raffle tickets to raise funds. The grand prize is a new laptop valued at $\mathrm{\backslash )}2,200$, the second prize is a bicycle worth $\mathrm{\backslash (}650$, and there are $12$ third prizes of $\mathrm{\backslash )}120$ gift cards. If $2,000$ tickets are sold, what is the expected value for a player who buys $1$ ticket?

A health magazine conducted a poll among $800$ readers about their weekly exercise habits. The question was, 'Do you exercise more than $3$ times a week?' The responses were collected as shown below.

Determine if the table represents a probability distribution, and if so, find its mean and standard deviation.

If the probabilities for all but one outcome in a discrete probability distribution are known, how can you find the missing probability?

Using the table below, what is the expected net winnings per spin (from the player’s point of view)? Round to three decimals.

A game has a probability distribution with $P\left(z\right)=0.25$ for $z$ values of $1,2,3,$ and $4$. Calculate the mean of the random variable $z$.

A survey of office workers recorded the number of password reset requests made by each employee in a month. The data below represents the probability distribution for the number of reset requests:

Is the random variable for the number of reset requests discrete or continuous? Explain.

What does a probability distribution table for a discrete random variable display?

In a small town library, there were $4380$ books loaned out over the course of $365$ days. Calculate the average number of books loaned out per day.

Given the following table, is it a valid probability distribution?x: 0, 1, 2, 3P(x): 0.2, 0.5, 0.1, 0.3