At Center Hospital there is some concern about the high turnover of nurses. A survey was done to determine how long (in months) nurses had been in their current positions. The responses (in months) of 20 nurses were

$$\begin{array}{cccccccccc} 23 & 2 & 5 & 14 & 25 & 36 & 27 & 42 & 12 & 8 \\ 7 & 23 & 29 & 26 & 28 & 11 & 20 & 31 & 8 & 36 \end{array}$$

Make a box-and-whisker plot of the data. Find the interquartile range.

Hurricane Damage Find the percentile rank for each value in the data set. The data represent the values in billions of dollars of the damage of $10$ hurricanes. \

$$1.1,1.7,1.9,2.1,2.2,2.5,3.3,6.2,6.8,20.3$$

What value corresponds to the $40$th percentile?

Consider the class of 30 students.

a. Find the probability that a randomly chosen student studies Spanish.

b. Find the probability that a randomly chosen student studies biology given that the student studies Spanish.

c. Are the events "student studies Spanish"' and "student studies biology", independent?

A hospital employs a total of 77 nurses and doctors. The ratio of nurses to doctors is 9:2. How many nurses are employed at the hospital? How many doctors are employed at the hospital?

a. Calculate the Euler approximation on the interval [0, 1] using n = 4 segments. Carry out the calculations “by hand” with the aid of a calculator, rounding calculations to two decimal places. Draw the graph of your approximation. b. Solve the differential equation and initial condition exactly by separating variables or using an integrating factor. c. Evaluate at x = 1 the solution that you found in part (b). Compare this actual value of y(1) (rounded to two decimal places) with the estimate for y(1) that you found in part (a). [Note: Expect low accuracy using n = 4.]

$$\begin{aligned} &y^{\prime}=\frac{4 x}{y}\\ &y(0)=1 \end{aligned}$$

The town of Butler, Nebraska, decided to give a teacher-competency exam and defined the passing scores to be those in the 70th percentile or higher. The raw test scores ranged from 0 to 100. Was a raw score of 82 necessarily a passing score? Explain.

Clayton and Timothy took different sections of Introduction to Economics. Each section had a different final exam. Timothy scored 83 out of 100 and had a percentile rank in his class of 72. Clayton scored 85 out of 100 but his percentile rank in his class was 70. Who performed better with respect to the rest of the students in the class, Clayton or Timothy? Explain your answer.

In your biology class, your final grade is based on several things: a lab score, scores on two major tests, and your score on the final exam. There are 100 points available for each score. However, the lab score is worth 25% of your total grade, each major test is worth 22.5%, and the final exam is worth 30%. Compute the weighted average for the following scores: 92 on the lab, 81 on the first major test, 93 on the second major test, and 85 on the final exam.

One standard for admission to Redfield College is that the student must rank in the upper quartile of his or her graduating high school class. What is the minimal percentile rank of a successful applicant?

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing, annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data.

$$\begin{array}{lllllllllll} x: & 11 & 0 & 36 & 21 & 31 & 23 & 24 & -11 & -11 & -21 \\ y: & 10 & -2 & 29 & 14 & 22 & 18 & 14 & -2 & -3 & -10 \end{array}$$

(c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. Use the intervals to compare the two funds.

The Grand Canyon and the Colorado River are beautiful, rugged, and sometimes dangerous. Thomas Myers is a physician at the park clinic in Grand Canyon Village. Dr. Myers has recorded (for a 5 -year period) the number of visitor injuries at different landing points for commercial boat trips down the Colorado River in both the Upper and Lower Grand Canyon. Upper Canyon: Number of Injuries per Landing Point Between North Canyon and Phantom Ranch 2 3 1 1 3 4 6 9 3 1 3 Lower Canyon: Number of Injuries per Landing Point Between Bright Angel and Lava Falls 8 1 1 0 6 7 2 14 3 0 1 13 2 1 Compute the mean, median, and mode for injuries per landing point in the Upper Canyon.

Wetlands offer a diversity of benefits. They provide a habitat for wildlife, spawning grounds for U.S. commercial fish, and renewable timber resources. In the last 200 years, the United States has lost more than half its wetlands. Environmental Almanac gives the percentage of wetlands lost in each state in the last 200 years. For the lower 48 states, the percentage loss of wetlands per state is as follows:

$$\scriptstyle\begin{array}{rrrrrrrrrr} 46 & 37 & 36 & 42 & 81 & 20 & 73 & 59 & 35 & 50 \\ 87 & 52 & 24 & 27 & 38 & 56 & 39 & 74 & 56 & 31 \\ 27 & 91 & 46 & 9 & 54 & 52 & 30 & 33 & 28 & 35 \\ 35 & 23 & 90 & 72 & 85 & 42 & 59 & 50 & 49 & \\ 48 & 38 & 60 & 46 & 87 & 50 & 89 & 49 & 67 & \end{array}$$

Make a stem-and-leaf display of these data. Be sure to indicate the scale. How are the percentages distributed? Is the distribution skewed? Are there any gaps?

Suppose you are looking at the 2006 results of how the Echo generation classified specified items as either luxuries or necessities. Do you expect the results to reflect how the Echo generation would classify items in 2020? Explain.

The mean time it takes a group of students to complete a statistics final exam is 44 minutes, and the standard deviation is 9 minutes. Within what limits would you expect approximately $95\%$ of the students to complete the exam? Assume the variable is approximately normally distributed.