At Fontaine Lake Camp on Lake Athabasca in northern Canada, history shows that about 30% of the guests catch lake trout over 20 pounds on a 4-day fishing trip. Let n be a random variable that represents the first trip to Fontaine Lake Camp on which a guest catches a lake trout over 20 pounds. What is the expected number of fishing trips that must be taken to catch the first lake trout over 20 pounds? Hint: Use m for the geometric distribution and round.

Gentle Ben is a Morgan horse at a Colorado dud ranch. Over the past 8 weeks, a veterinarian took the following glucose readings from this horse (in mg/100 ml).

$$93 \quad 88 \quad 82 \quad 105 \quad 99 \quad 110 \quad 84 \quad 89$$

The sample mean is $\bar{x} \approx 93.8$. Let x be a random variable representing glucose readings taken from Gentle Ben. We may assume that x has a normal distribution, and we know form past experience that $\sigma = 12.5$. The mean glucose level for horses should be $\mu=85 \mathrm{mg} / 100 \mathrm{ml}$. Do these data indicate that Gentle Ben has an overall average glucose level higher than 85? Use $\alpha=0.05$. What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?

A motion picture industry analyst is studying movies based on epic novels. The following data were obtained for JO Hollywood movies made in the past 5 years. Each movie was based on an epic novel. For these data, $x_1$= first-year box office receipts of the movie, $x_2$ = total production costs of the movie, $x_3$ = total promotional costs of the movie, and $x_4$ = total book sales prior to movie release. All units are in millions of dollars.

$$\begin{matrix} \text{}{x_{1}} & \text{}{x_{2}} & \text{}{x_{3}} & \text{}{x_{4}} & \text{}{x_{1}} & \text{}{x_{2}} & \text{}{x_{3}} & \text{}{x_{4}}\\ \text{85.1} & \text{8.5} & \text{5.1} & \text{4.7} & \text{30.3} & \text{3.5} & \text{1.2} & \text{3.5}\\ \text{106.3} & \text{12.9} & \text{5.8} & \text{8.8} & \text{79.4} & \text{9.2} & \text{3.7} & \text{9.7}\\ \text{50.2} & \text{5.2} & \text{2.1} & \text{15.1} & \text{91.0} & \text{9.0} & \text{7.6} & \text{5.9}\\ \text{130.6} & \text{10.7} & \text{8.4} & \text{12.2} & \text{135.4} & \text{15.1} & \text{7.7} & \text{20.8}\\ \text{54.8} & \text{3.1} & \text{2.9} & \text{10.6} & \text{89.3} & \text{10.2} & \text{4.5} & \text{7.9}\\ \end{matrix}$$

Perform a regression analysis with $x_{4}$ as the response variable. Use $x_{1}, x_{2}$, $x_{3}$ as explanatory variables. Look at the coefficient of multiple determination. What percentage of the variation in $x_{4}$ can be explained by the corresponding variations in $x_{1}, x_{2}$ and $x_{3}$ taken together?

Find the derivative of each function by using the Quotient Rule. Simplify your answers. $f(x)=\frac{x^{2}-2 x+3}{x+1}$

In an issue of Discover, J. Netting described the research of E. Tibbetts of the University of Arizona in the article, "The Kind of Face Only a Wasp Could Trust." Tibbetts found that wasps signal their strength and status with the number of black splotches on their yellow faces, with more splotches denoting higher status. Tibbetts decided to see if she could cheat the system. She painted some of the insects' faces to make their status appear higher or lower than it really was. She then placed the painted wasps with a group of female wasps to see if painting the faces altered their hierarchical status. Was this investigation an observational study or a designed experiment? Justify your answer.

If the lens of the eye becomes cloudy and impairs vision, the condition is called a _____.

For the four small data sets given here, indicate which has the smallest standard deviation and which has the largest without performing any calculations. Justify your answer. Set 1: 1, 1, 1, 9, 9, 9; Set 2: 1, 1, 1, 6, 6, 6, 9, 9, 9; Set 3: 3,4,5,6,7,8,9; Set 4: 3, 4, 5, 6, 6, 6, 7, 8, 9.

_____, _____, _____, _____, and _____ are the five levels of organization in a living thing.

Curing times in days (x) and compressive strengths in MPa (y) were recorded for several concrete specimens. The means and standard deviations of the x and y values were $\bar{x}=5, s_{x}=2, \bar{y}=1350, s_{y}=100.$ The correlation between curing time and compressive strength was computed to be r = 0.7. Find the equation of the least-squares line to predict compressive strength from curing time.

Evaluate each iterated integral. $\int_{0}^{2} \int_{-x}^{x}\left(x^{2}-y\right) d y d x$

The article “Traps in Mineral Valuations—Proceed With Care" models the value (in millions of dollars) of a mineral deposit yet to be mined as a random variable X with probability mass function p(x) given by p(10) = 0.40, p(60) = 0.50, p(80) = 0.10, and p(x) = 0 for values of x other than 10, 60, or 80. a. Is this article treating the value of a mineral deposit as a discrete or a continuous random variable? b. Compute $\mu_{x}.$ c. Compute $\sigma_{X}.$ d. The project will be profitable if the value is more than $50 million. What is the probability that the project is profitable?

In baseball, is there a linear correlation between batting average and home run percentage? Let x represent the batting average of a professional baseball player, and let y represent the player 's home run percentage (number of home runs per 100 times at bat). A random sample of n = 7 professional baseball players gave the following information.

$$\begin{matrix} \text{x} & \text{0.243} & \text{0.259} & \text{0.286} & \text{0.263} & \text{0.268} & \text{0.339} & \text{0.299}\\ \text{y} & \text{1.4} & \text{3.6} & \text{5.5} & \text{3.8} & \text{3.5} & \text{7.3} & \text{5.0}\\ \end{matrix}$$

Make a scatter diagram and draw the line you think best fits the data.

The owners of a motel in Florida have noticed that in the long run, about 40% of the people who stop and inquire about a room for the night actually rent a room. If 25 separate inquiries are made about rooms, what is the expected number of inquiries that will result in room rentals?

Tempe thinks she's pretty skilled at "mouth-catching" (no hands) bits of snack food that have been thrown to her from across a room. She wonders, though, if she's better at catching some foods than others, so she conducts an experiment. A friend tosses 150 pieces of each of three different kinds of snack food (in random sequence) and then records how often Tempe catches the food in her mouth. Here are the results.

$$\begin{array} {lc} & \text{Snack food} \\ \text {Caught?} &\begin{array}{l|c|c|c|c} & \text { Goldfish } & \text { Grapes } & \text { Gummies } & \text { Total } \\ \hline \text { Yes } & 90 & 100 & 115 & 305 \\ \hline \text { No } & 60 & 50 & 35 & 145 \\ \hline \text { Total } & 150 & 150 & 150 & 450 \end{array} \\ \end{array}$$

Identify the explanatory and response variables.