Customers in a Bank A bank has a drive-through service. The number of customers arriving during a $15$-minute period is distributed as shown. Find the mean. variance, and standard deviation for the distribution.

$$\begin{array}{l|ccccc} \textbf{Number of customers} X & 0 & 1 & 2 & 3 & 4 \\ \hline \textbf{Probability} P(X) & 0.12 & 0.20 & 0.31 & 0.25 & 0.12 \end{array}$$

A box contains 5 pennies, 3 dimes, 1 quarter, and 1 half-dollar. A coin is drawn at random. Construct a probability distribution and draw a graph for the data.

Poverty and the Federal Government One out of every three Americans believes that the U.S. government should take "primary responsibility" for eliminating poverty in the United States. If $10$ Americans are selected, find the probability that at most $3$ will believe that the U.S. government should take primary responsibility for eliminating poverty.

Survey on Bathing Pets A survey found that $25 \%$ of pet owners had their pets bathed professionally rather than do it themselves. If $18$ pet owners are randomly selected, find the probability that exactly $5$ people have their pets bathed professionally.

Find the mean, variance, and standard deviation for each of the values of $n$ and $p$ when the conditions for the binomial distribution are met. \

$$n=10, p=0.8$$

Find the mean, variance, and standard deviation for each of the values of $n$ and $p$ when the conditions for the binomial distributions are met. \

$$n=36, p=\frac{1}{6}$$

A circuit to run a model railroad has 8 switches. Two are defective. If you select 2 switches at random and test them, find the probability that the second one is defective, given that the first one is defective.

At a convention there are 7 mathematics instructors, 5 computer science instructors, 3 statistics instructors, and 4 science instructors. If an instructor is selected, find the probability of getting a science instructor or a math instructor.

A student takes a 20-question, multiple-choice exam with five choices for each question and guesses on each question. Find the probability of guessing at least 15 out of 20 correctly. Would you consider this event likely or unlikely to happen? Explain your answer.

A large retail company encourages its employees to get customers to apply for the store credit card.

Below is the distribution for the number of credit card applications received per employee for an 8-hour shift.

$$\begin{array}{l|cccccc} \boldsymbol{X} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \boldsymbol{P}(\boldsymbol{X}) & 0.27 & 0.28 & 0.20 & 0.15 & 0.08 & 0.02 \end{array}$$

a. What is the probability that an employee will get 2 or 3 applications during any given shift?

b. Find the mean, variance, and standard deviation for this probability distribution.

Credit Cards A large retail company encourages its employees to get customers to apply for the store credit card. Below is the distribution for the number of credit card applications received per employee for an $8$-hour shift.

$$\begin{array}{l|cccccc} \boldsymbol{X} & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline \boldsymbol{P}(\boldsymbol{X}) & 0.27 & 0.28 & 0.20 & 0.15 & 0.08 & 0.02 \end{array}$$

Find the mean, variance, and standard deviation for this probability distribution.

Emergency Calls The number of emergency calls that a local police department receives per $24$-hour period is distributed as shown here. Construct a graph for the data.

$$\begin{array}{l|ccccc} \textbf{Number of calls} X & 10 & 11 & 12 & 13 & 14 \\ \hline \textbf{Probability} P(X) & 0.02 & 0.12 & 0.40 & 0.31 & 0.15 \end{array}$$

Compute the probability of $X$ successes, using Table $B$ in Appendix $\mathrm{A}$. \

$$n=16, p=0.20, X=3$$

Find the mean, variance, and standard deviation for each of the values of $n$ and $p$ when the conditions for the binomial distribution are met. \

$$n=300, p=0.3$$