New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night. Suppose that room rates are normally distributed with a standard deviation of $55.

a. What is the possibility that a hotel room costs $225 or more per night?

A fast-food restaurant chain has 600 outlets in the United States. The following table categorizes cities by size and location, and presents the number of restaurants in cities of each category. A restaurant is to be chosen at random from the 600 to test market a new style of chicken.

$$\begin{array}{lrrrr} \hline & & & {\text { Region }} \\ \hline \text { Population of City } & \text { NE } & \text { SE } & \text { SW } & \text { NW } \\ \hline \text { Under } 50,000 & 30 & 35 & 15 & 5 \\ 50,000-500,000 & 60 & 90 & 70 & 30 \\ \text { Over } 500,000 & 150 & 25 & 30 & 60 \\ \hline \end{array}$$

a. If the restaurant is located in a city with a population over 500,000, what is the probability that it is in the Northeast? b. If the restaurant is located in the Southeast, what is the probability that it is in a city with a population under 50,000? c. If the restaurant is located in the Southwest, what is the probability that it is in a city with a population of 500,000 or less? d. If the restaurant is located in a city with a population of 500,000 or less, what is the probability that is in the Southwest? e. If the restaurant is located in the South (either SE or SW), what is the probability that it is in a city with a population of 50,000 or more?

New York City is the most expensive city in the United States for lodging. The mean hotel room rate is $204 per night (USA Today, April 30, 2012). Assume that room rates are normally distributed with a standard deviation of$55. a. What is the probability that a hotel room costs $225 or more per night?

For lodging, New York City is the most expensive city in the United States. The average hotel room cost is $\$204$ per night (USA Today, April 30, 2012). Assume that room rates follow a normal distribution with a standard deviation of $\$ 55$. a. What is the probability that a hotel room will cost $\$225$ or more per night? b. What is the probability that a hotel room will cost less than $\$140$ per night? c. What is the probability that a hotel room will cost between $\$200$ and $\$300$ per night? d. What is the cost of the $20 \%$ most expensive hotel rooms in New York City?

What is the cost of the 20% most expensive hotel rooms in New York City?

In the given problems may involve combinations, permutations, or the fundamental counting principle.

The fire inspector in Cincinnati must select three night clubs from a list of eight for an inspection of their compliance with the fire code. In how many ways can she select the three night clubs?

A simple random sample of 50 items from a population with $\sigma=6$ resulted in a sample mean of 32 .

c. Provide a $99 \%$ confidence interval for the population mean.

The planners for a new section of the city want every location on Main Street to be equidistant from Elm Street and Grove Street. How can the planners ensure that this is the case?

Make an order-of-magnitude estimate of the quantity. -The time interval needed to drive nonstop from San Francisco to New York City by the most direct route.

the positively oriented simple closed curve C for which the value of the line integral $\int_{C}\left(y^{3}-y\right) d x-2 x^{3} d y$ is a maximum.

During Stage 1 light sleep, a person is most likely to experience a. sleep spindles. b. hallucinations. c. night terrors or nightmares. d. rapid eye movements.

You are going to use the Correlation and Regression applet to make different scatterplots with 10 points that have correlation close to 0.8. Many patterns can have the same correlation. Always plot your data before you trust a correlation. (a) Stop after adding the first 2 points. What is the value of the correlation? Why does it have this value no matter where the 2 points are located? (b) Make a lower-left to upper-right pattern of 10 points with correlation about $r=0.8$. (You can drag points up or down to adjust $r$ after you have 10 points.) Make a rough sketch of your scatterplot. (c) Make another scatterplot, this time with 9 points in a vertical stack at the left of the plot. Add one point far to the right and move it until the correlation is close to 0.8. Make a rough sketch of your scatterplot. (d) Make yet another scatterplot, this time with 10 points in a curved pattern that starts at the lower left, rises to the right, then falls again at the far right. Adjust the points up or down until you have a quite smooth curve with correlation close to 0.8. Make a rough sketch of this scatterplot also.

In laparoscopic surgery, a video camera and several thin instruments are inserted into the patient's abdominal cavity. The surgeon uses the image from the video camera positioned inside the patient's body to perform the procedure by manipulating the instruments that have been inserted. It has been found that the Nintendo Wii$^\text{™}$, with its motion-sensing interface, reproduces the movements required in laparoscopic surgery more closely than other video games. If training with a Nintendo Wii$^\text{™}$ can improve laparoscopic skills, it can complement the more expensive training on a laparoscopic simulator. Forty-two medical residents were chosen and all were tested on a set of basic laparoscopic skills. Twenty-one were selected at random to undergo systematic Nintendo Wii$^\text{™}$ training for one hour a day, five days a week, for four weeks. The remaining 21 residents were given no Nintendo Wii$^\text{™}$ training and asked to refrain from video games during this period. At the end of four weeks, all 42 residents were tested again on the same set of laparoscopic skills. The difference in time (before - after) to complete a virtual gall bladder removal on the simulator was measured.

(a) Compare the study described above with the study in the given example. What are the important differences between the two studies? Ignoring the fact that different video games and measures of laparoscopic skill were used in the two studies, explain in simple language which study gives stronger evidence that playing video games is helpful in improving laparoscopic skills and why.

(b) Outline the design of this experiment, following the model of the given figure. What is the response variable?

(c) Carry out the random assignment of 21 residents to the Nintendo training group, using the Simple Random Sample applet, other software, or table of random digits, starting at line 130.

Estimate how many solar neutrinos pass through a $180 \mathrm{~m}^2$ ceiling of a room, at latitude $44^{\circ}$, for an hour around midnight on midsummer night.