Grade 9 · Statistics & probability

Problem solving in context (SAT) practice

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 5050 warehouse workers at random from all 600600 workers at a distribution center. She found that 3535 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 3550=710\dfrac{35}{50} = \dfrac{7}{10}. The best estimate for the center is 710×600=420\dfrac{7}{10} \times 600 = 420 workers.

Question 2easy

A botanist chose 2424 seedlings at random from a field of 360360 seedlings. Of the seedlings in the sample, 1818 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 1824=34\dfrac{18}{24} = \dfrac{3}{4}. The best estimate for the field is 34×360=270\dfrac{3}{4} \times 360 = 270 seedlings.

Question 3easy

A librarian checked 4040 books selected at random from a collection of 800800 books. She found that 1414 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 1440=720\dfrac{14}{40} = \dfrac{7}{20}. The best estimate for the collection is 720×800=280\dfrac{7}{20} \times 800 = 280 books.

Question 4easy

A stone is thrown upward from the edge of a cliff overlooking a valley. The equation s=5t2+11t+16s = -5t^2 + 11t + 16 models the stone's height ss, in meters, above the valley floor tt 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=0t = 0. Then s=5(0)2+11(0)+16=16s = -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+64d = -16t^2 + 48t + 64 represents this situation, where dd is the height of the football above the field, in feet, tt 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=0t = 0. Substituting gives d=16(0)2+48(0)+64=64d = -16(0)^2 + 48(0) + 64 = 64 feet.

Question 6medium

A grocer surveyed 2525 customers selected at random and found that 1515 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 500500 who would purchase at least one organic item?

The sample proportion is 1525=35\dfrac{15}{25} = \dfrac{3}{5}. The best estimate for 500500 customers is 35×500=300\dfrac{3}{5} \times 500 = 300 customers.

Question 7medium

A function pp estimates that a town had 8,4008{,}400 residents in 20102010. Each year from 20102010 through 20202020, the function estimates that the population increased by 2%2\% of the population the previous year. Which equation defines this function, where p(x)p(x) is the estimated population xx years after 20102010?

The initial population is 8,4008{,}400, and a 2%2\% yearly increase means multiplying by 1.021.02, so p(x)=8,400(1.02)xp(x) = 8{,}400(1.02)^x.

Question 8medium

A function ww estimates that there were 2,5002{,}500 nesting pairs of birds in a wetland in 20052005. Each year from 20052005 through 20162016, the function estimates that the number of nesting pairs increased by 4%4\% of the number the previous year. Which equation defines this function, where w(x)w(x) is the estimated number of nesting pairs xx years after 20052005?

The starting count is 2,5002{,}500, and a 4%4\% yearly increase means multiplying by 1.041.04, so w(x)=2,500(1.04)xw(x) = 2{,}500(1.04)^x.

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