Directions: Choose the best answer to each question.

1. Eva lives in Wyoming which has a general state sales tax on purchases. If Eva buys a car for $18,000, how much money will she pay in sales tax? A.$180 B. $900 C.$1,800 D. Not enough information is given.

In an attempt to increase sales, a breakfast cereal company decides to offer a promotion. Each box of cereal will contain a collectible card featuring one NASCAR driver: Kyle Busch; Dale Earnhardt, Jr.; Kasey Kahne; Danica Patrick; or Jimmie Johnson. The company says that each of the 5 cards is equally likely to appear in the 100,000 boxes of cereal that are part of this promotion. You buy 12 boxes and let X = the number of Kyle Busch cards in the sample. Calculate the mean and standard deviation of the sampling distribution of X.

Choose the best answer for each question.

Which would not cause a density current?

(a) trade winds

(b) evaporation

(c) freezing

Choose the best answer for each question. Which county official enforces court orders? A. assessor. B. coroner. C. district attorney. D. sheriff.

Which three areas of the world have the highest population growth rate? Which three areas of the world have the lowest standard of living?

Find each integral. $\int \csc ^{2} \pi t d t$

Based on long experience, an airline has found that about 6% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 267 ticket reservations for an airplane with only 255 seats. Let n = 267 represent the number of ticket reservations. Let r represent the number of people with reservation s who show up for the flight. Which expression represents the probability that a seat will be available for everyone who shows up holding a reservation? $P(255 \leq r)$; $P(r \leq 255)$; $P(r \leq 267)$; $P(r=255)$

Your teacher brings two large bags of colored goldfish crackers to class. Bag 1 has 25% red crackers and Bag 2 has 35% red crackers. Using a paper cup, your teacher takes an SRS of 50 crackers from Bag 1 and a separate SRS of 40 crackers from Bag 2. Let $\hat{p}_{1}-\hat{p}_{2}$ be the difference in the sample proportions of red crackers. What is the shape of the sampling distribution of $\hat{p}_{1}-\hat{p}_{2} ?$ Why?

For any cumulative distribution function F(x), show that if $a \leq b,$ then $F(a) \leq F(b)$

You do not need a lot of money to invest in a mutual fund. However, if you decide to put some money into an investment, you are usually advised to leave it in for (at least) several years. Why? Because good years tend to cancel out bad years, giving you a better overall return with less risk. To see what we mean, let's use a 3-year moving average on the Calvert Social Balanced Fund (a socially responsible fund). $$ \begin{array}{l|rrrrrr} \hline \text { Year } & 1990 & 1991 & 1992 & 1993 & 1994 & 1995 \\ \hline \text { % Return } & 1.78 & 17.79 & 7.46 & 5.95 & -4.74 & 25.85 \\ \hline \end{array} $$ $$ \begin{array}{ccccc} \hline \text{Year} & 1996 & 1997 & 1998 & 1999 & 2000 \\ \hline \text{\\% Return} &9.03 & 18.92 & 17.49 & 6.80 & -2.38 \\ \hline \end{array} $$ Use a calculator with mean and standard deviation keys to verify that the mean annual return for all 11 years is approximately 9.45%, with standard deviation 9.57%.

Assuming that the null hypothesis $H_{0}$: $\eta=\eta_{0}$ is true, answer the following questions. a. Why is the probability of an observation exceeding $\eta_{0}$ equal to 0.5? b. In a simple random sample of size n, why does the number of observations that exceed $\eta_{0}$ have a binomial distribution with parameters n and 0.5?

Use integration by parts to find each integral. $\int s(2 s+1)^{4} d s$

For a binomial experiment, what probability distribution is used to find the probability that the first success will occur on a specified trial?

Do seagulls show a preference for where they land? To answer this question, biologists conducted a study in an enclosed outdoor space with a piece of shore made up of 56% sand, 29% mud, and 15% rocks. The biologists chose 200 seagulls at random. Each seagull was released into the outdoor space on its own and observed until it landed somewhere on the piece of shore. In all, 128 seagulls landed on the sand, 61 landed in the mud, and 11 landed on the rocks. Calculate the value of the chi-square test statistic for these data.