Problem solving in context (SAT) is a grade 9 math skill aligned to Common Core standard HSS.IC.B.4: use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 problem solving in context (sat) problems our math games drill.
CCSS HSS.IC.B.410 questions in the bank
Sample questions
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Question 1easy
Elena selected 50 warehouse workers at random from all 600 workers at a distribution center. She found that 35 of the workers in this sample wore required safety gear during their shift. Based on Elena's findings, which of the following is the best estimate of the number of workers at the center who wore required safety gear during their shift?
The sample proportion is 5035=107. The best estimate for the center is 107×600=420 workers.
Question 2easy
A botanist chose 24 seedlings at random from a field of 360 seedlings. Of the seedlings in the sample, 18 had sprouted. Based on this sample, which of the following is the best estimate of the number of seedlings in the field that had sprouted?
The sample proportion is 2418=43. The best estimate for the field is 43×360=270 seedlings.
Question 3easy
A librarian checked 40 books selected at random from a collection of 800 books. She found that 14 of the books in the sample were fiction. Based on the sample, which of the following is the best estimate of the number of fiction books in the collection?
The sample proportion is 4014=207. The best estimate for the collection is 207×800=280 books.
Question 4easy
A stone is thrown upward from the edge of a cliff overlooking a valley. The equation s=−5t2+11t+16 models the stone's height s, in meters, above the valley floor t seconds after it is thrown. According to the equation, what is the height, in meters, of the cliff edge above the valley floor?
When the stone is thrown from the cliff edge, t=0. Then s=−5(0)2+11(0)+16=16 meters above the valley floor.
Question 5easy
A football is kicked from a stadium deck. The equation d=−16t2+48t+64 represents this situation, where d is the height of the football above the field, in feet, t seconds after it is kicked. According to the equation, what is the height, in feet, of the deck from which the football was kicked?
When the kick occurs, t=0. Substituting gives d=−16(0)2+48(0)+64=64 feet.
Question 6medium
A grocer surveyed 25 customers selected at random and found that 15 of them purchased at least one organic item. Based on the survey, which of the following is the best estimate of the number of customers out of 500 who would purchase at least one organic item?
The sample proportion is 2515=53. The best estimate for 500 customers is 53×500=300 customers.
Question 7medium
A function p estimates that a town had 8,400 residents in 2010. Each year from 2010 through 2020, the function estimates that the population increased by 2% of the population the previous year. Which equation defines this function, where p(x) is the estimated population x years after 2010?
The initial population is 8,400, and a 2% yearly increase means multiplying by 1.02, so p(x)=8,400(1.02)x.
Question 8medium
A function w estimates that there were 2,500 nesting pairs of birds in a wetland in 2005. Each year from 2005 through 2016, the function estimates that the number of nesting pairs increased by 4% of the number the previous year. Which equation defines this function, where w(x) is the estimated number of nesting pairs x years after 2005?
The starting count is 2,500, and a 4% yearly increase means multiplying by 1.04, so w(x)=2,500(1.04)x.
Tests that cover problem solving in context (sat):