In managing your monthly budget, you allocate your income across various categories such as rent, groceries, entertainment, and savings. Each category contributes differently to your overall financial health. Rent takes up 22.5% of your income, groceries 22.5%, entertainment 30%, and you aim to save 25%. Compute the weighted average allocation for the following amounts: $1000 for rent, $200 for groceries, $130 for entertainment, and $400 for savings. Round your answer to the nearest dollar.  

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   24 2 5 16 26 37 28 48 14 8 6 24 32 27 29 11 22 33 9 37 ​ A box-and-whisker plot of the data is shown below.     Find the interquartile range.

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 the coefficient of variation for each fund. Round your answers to the nearest tenth.   x: 12 0 39 23 35 25 26 –12 –12 –15 y: 10 –4 27 15 24 18 15 4 –5 –10 ​ ​

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 the sample variance for variable x. Round your answer to two decimal places.   14 0 35 25 29 27 28 –14 –14 –25 6 –5 13 17 26 6 17 –5 –6 –6 ​

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 is from the West given that he or she has been loyal from 3 to 4 years? Round your answer to the nearest thousandth.

Diagnostic tests of medical conditions have several results. The rest result can be positive or negative. A positive test (+) indicates the patient has the condition. A negative test (–) indicates the patient does not have the condition. Remember, a positive test does not prove the patient has the condition. Additional medical work may be required. Consider a random sample of 200 patients, some of whom have a medical condition and some of whom do not. Results of a new diagnostic test for the condition are shown.     Condition Present Condition Absent Row Total Test Result + 109 21 130 Test Result – 21 49 70 Column Total 130 70 200 ​ Assume that the sample is representative of the entire population. For a person selected at random, find P(getting test result – and condition absent). Round your answer to the nearest hundredth.

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 ​