Please solve and show all work. use this link when the question asks you to: https://www12.statcan.gc.ca/census-recensement/2016/dp-pd/dv-vd/inc-rev/index-eng.cfm

1. In order to proceed with this rst problem, you'll require the concept of percentiles. By way of example, consider the yearly incomes earned by Canadians in 2016, according to the 2016 Census Data. Note that 80% of Canadians {aged 15 or over) earned a yearly income less than or equal to $68,332. We could then correctly write the following sentences: o Among all yearly incomes for Canadians (aged 15 or over) in 2016, the 80th percentile was $68,332. 0 For a Canadian in 2016 earning a yearly income of $68,332 in 2016, their percentile male was 80%. It is also common to say that their income is in the 80th percentile. In this context, note that a percentile is an income in dollars. On the other hand, the percentile rank is a percentage. It may also be helpful to note that the 50th percentile is also lcnown as the median. 50% of people earn less than the median income and 50% of people earn more than the median income. (a) Open up the 2016 Census Data: https://ww12 .statcan.gc . ca/censue-recensement/ZOlS/dp-pd/ dv-vd/inc-rev/ index-sag. cfm. View the age category that opens by default, then click to view the data table below the graph. Use the data table to ll in the blanks below. o Among the incomes for Canadian adults of age 19, the 25th percentile is :l, the a... :l and M... :- u lfa 25-year old Canadian makes $25K er r, what is their percentile rank for their age? They are approximately in the h percentile. (You may round to the nearest 5.) II 5% of 30-year old Canadians make an income greater than I. Percentiles are often used to describe data in many contexts! For the rest of this problem, you'll consider the weights and lengths of male and female infants. Infant growth: By regularly weighing and measuring an infant, their parents and doctors can use infant weight-for-length charts to gauge how well the infant is growing. Please use the following link to view data tables for infant weight-forlength charts: https://www.cdc.gov/growthcharts/html_charts/wtleninf.htm. (b) The second table concerns female infants and represents a function f of two variables, L and P. If L represents an infant's length and P is a percentage, what does f(L,P) represent? Please write your answer in the form of a sentence in the box below. (c) The parents of a female infant notice from the chart that f {48.5, 10') = 2.595089. If they ask you what this means, how would you reply? {Make sure that your answer is in the form of a plain English sentence that the parents would easily understand.) (d) Imagine that you are a medical doctor. You've just measured a female infant to be 55.5 cm long, with a weight of 5.00 kg. Using the chart for female infants, what might you tell her parents? \"Your daughter's weight is the |:'th percentile, for her length. This means that she is heavier than I% of female infants of the same length.\" (e) The data in the two charts is in an excel spreadsheet that you can download from quercus. This allows you to plot and discuss cross-sections of the charts, if you wish. Here are the plots of the nine cross-sections, f{L,3), f{L,5), . . . ,f(L,97). 18 16 \"00m 1'! IDI ii. iii. iv. . In each of the two boxes above, please write a short axis label, including the units in brackets. The curves are labelled with letters. 'Which letter labels the curve corresponding to KL, 3)? I Which letter labels the curve corresponding to f (12,50)? I Which letter labels the curve corresponding to f (12,95)? I Imagine a set of female triplets, who are all 63.5 cm tall, but one is thin, one is of average weight, and one is heavy. Mark 3 possible points with an x in the above gure, that could represent their measurements. Make sure they are easy for the grader to see. If a female infant has approximately average weight for her length, mark three different points which could represent her measurements with an X on the graph below {which is a copy of the graph above). 20- "00m 11 n: H- I2 (f) Here are the plots of eight cross-sections, f (45.5, P), f(48.5, P), f(51.5, P), f(54.5, P), f(57.5, P), f(60.5, P), f (63.5, P), and f (66.5, P). 10 9 7 T O I ( ) m W O 10 20 30 40 50 60 70 80 90 100 i. In each of the two boxes above, please write a short axis label, including the units in brackets. ii. The curves are labelled with letters. Which letter labels the curve corresponding to f (48.5, P)? Which letter labels the curve corresponding to f (60.5, P)? Which letter labels the curve corresponding to f (66.5, P)? iii. Imagine a set of female triplets, who are all 63.5 cm tall, but one is thin, one is of average weight, and one is heavy. Mark 3 possible points with an x in the above figure, that could represent their measurements. Make sure they are easy for the marker to see. (g) Suppose that a doctor's office asks you to create a poster for new parents, representing weight-for-length data for infants. Choosing between the figures in parts (e) and (f), which set of cross-sections might you put on the poster? Please fill in the blank and then explain your answer in the box below. I would include the set of cross-sections from part on the poster.2. A Hungry Student A student has only three things in her cupboard: poptarts, trail mix, and beef jerky. She needs a meal with 1450 calories, 50 grams of fat, and 180 mg of sodium. Per serving, poptarts have 200 calories, 10 grams of fat, and 30 nag of sodium. Per 50-gram serving, trail mix has 150 calories, 5 grams of fat, and 15 mg of sodium. Per IUD-gram serving, beef jerky has 550 calories, 20 grams of fat, and 60 nag of sodium. (a) The student will construct her meal by solving a linear algebra problem, with ':| equations and l variables. Please ll in the blanks and then write the linear system below. Be sure to also clearly dene each variable and indicate what each equation represents. (Use units of servings for food.) (b) What is the augmented matrix for this problem? Please reduce this matrix to Reduced Row Echelon Form. Be sure to label all of your row operations. Hint: the computations to nd the RREF may be much. easier if you exchange certain miss rst. Take a moment to strategize before before you begin. (c) Find a general solution in parametric form. (Please call your parameter t.) In plain English, what does your solution represent in terms of servings of poptarts, 50-gram servings of trail mix, and IOU-gram servings of beef jerky? (d) At the level of solutions to linear algebra problems, the parameter t in your solution can generally take on any value. But in terms of food in the cupboard, it can't, even with a very large supply of all three items in the cupboard. For realistic solutions, what range of values can your parameter take? Why? The parameter must lie in the range ':I g t g |:|. (e) Poptarts cost $1.50 per serving, trail mix costs $2 per serving, and beef jerky costs $8 per serving. i. Using your intuition, can you predict the composition of the cheapest meal and most expensive meal? Discuss this with your pod. (You do not need to record your conversation here.) ii. Find the cost and composition of the cheapest meal, in terms of servings of pop tarts, trail mix and beef jerkey. Hint: Start by nding a formula for the total meal cost as a function of the parameter, C (t) Show your reasoning and state your nal answers below. The cheapest meal would be comprised of servings of poptarts, 50-gram servings of trail mix, and IOU-gram servings of beef jerkey. The cheapest meal costs dollars