You want to make a salad from whatever vegetable you have in the fridge. You have seven different tomatoes. There are 2 red tomatoes, 4 yellow tomatoes, and one black tomato in the fridge. You have three different bell peppers. There is 1 red pepper, 1 yellow pepper, and 1 green pepper. What is the probability of randomly choosing a vegetable and getting a red tomato, and a green pepper? Round your answer to four decimal places.  

It is thought that prehistoric Native Americans did not take their best tools, pottery, and household items when they visited higher elevations for their summer camps. It is hypothesized that archaeological sites tend to lose their cultural identity and specific cultural affiliation as the elevation of the site increases. Let x be the elevation (in thousands of feet) for an archaeological site in the southwestern United States. Let y be the percentage of unidentified artifacts (no specific cultural affiliation) at a given elevation. Suppose that the following data were obtained for a collection of archaeological sites in New Mexico:   x 5.25 5.75 6.75 7.00 8.00 y 26 56 75 86 80 ​ Calculate the sample correlation coefficient r. Round your answer to three decimal places.  

Compute the population variance

Are tech stocks more volatile than utility stocks? Let x be a random variable representing the annual percent return for a portfolio of technology stocks. Let y be a random variable representing the annual percent return for a portfolio of utility stocks. For the past few years, assume the following data. Compute a 75% Chebyshev interval around the mean for x-values and y-values. Round your answers to the nearest hundredth. ​ x: 11 0 35 20 24 22 23 –11 –11 –20 y; 8 –4 28 14 21 16 14 –4 –5 –8 ​

Given the sample data below, use the defining formula to compute the sample standard deviation.   13 19 29 15 12 29

Does the size of a company’s IT department impact its cybersecurity incident rate? Let x represent the number of IT staff members, and let y represent the cybersecurity incident rate per year. Suppose a random sample of companies provided the following information. x 2 8 14 32 73 y 50 45 35 28 16 As x increases, does the value of r imply that y should tend to increase, decrease, or remain the same? Explain.

Are customers more loyal in the East or in the West? The following table is based on information from Trends in the United Sates, published by the food marketing Institute, Washington, D.C. The columns represent loyalty (in years) at a primary supermarket. The rows represent regions of the United States.     Less Than 1 Year  1 – 2 Years 3 – 4 Years 5 – 9 Years 10 – 14 Years 15 or More Years Row Total East 32 54 59 112 77 118 452 Midwest 31 68 68 120 63 173 523 South 53 92 93 158 106 158 660 West 41 56 67 78 45 86 373 Column Total 157 270 287 468 291 535 2008 ​ What is the probability that a customer chosen at random has been loyal from 3 to 4 years given that he or she is from the South? Round your answer to the nearest thousandth.

Identify the sampling technique used in the following information. ​ Suppose you are conducting a survey to study the commuting patterns of residents in a metropolitan area. You want to understand the modes of transportation used by residents, including carpooling, public transportation, cycling, walking, and telecommuting. You plan to survey 200 residents across different neighborhoods using various sampling techniques. Categorize each technique as a simple random sample, stratified sample, systematic sample, cluster sample, or convenience sample. Group the residents based on their workplace location: downtown, suburban business parks, industrial areas, residential neighborhoods, and remote work setups. Then randomly select 10 residents from each workplace location category for the survey. ​

Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the range for variable x.   15 0 37 23 33 25 26 -15 -15 -23 6 -1 28 18 24 17 18 -1 -2 -6

Identify the variable in the information below. ​ Consider a wildlife reserve known for its diverse ecosystem. Researchers are interested in understanding the distribution of a specific species of birds within the reserve. To estimate the population density of these birds, a random sample of 60 observation points, each covering an area of 200 square meters, is selected. The researchers record the number of bird nests in each observation point as an indicator of the bird population density in the region.