Predicting from Samples

Additional Example 3: Verifying Claims Based on Statistical Data A principal of a school with 1,500 students estimates that about 400 students will attend a band festival on Saturday. A random sample of 25 students showed that 6 of them will attend. Determine whether the principal’s estimate is likely to be accurate. Set up a proportion to predict the total number of students that will attend. Students attending sample # of Students sampled Students attending Student Population = 2

Additional Example 3 Continued 6 25 x 1500 Let x represent the number of actual students attending the band festival. = 6 • 1500 = 25 • x The cross products are equal. 9000 = 25x Multiply. 9000 25 25x 25 = Divide each side by 25 to isolate x. 360 = x The estimate is not accurate because the data shows that 360 students are likely to attend. 3

Check It Out: Example 3 The owner of a large chain restaurant with 1,200 employees estimates that about 250 employees will ask for winter vacation. A random sample of 40 employees showed that 8 of them will ask for the time off. Determine whether the owner’s estimate is likely to be accurate. Set up a proportion to predict the total number of students that will attend. Employees surveyed for time off # of Employees surveyed Employees asking for time off Total # of Employees = 4

Check It Out: Example 3 Continued 8 40 x 1200 Let x represent the number of actual employees asking for time off. = 8 • 1200 = 40 • x The cross products are equal. 9600 = 40x Multiply. 9600 40 40x 40 = Divide each side by 40 to isolate x. 240 = x The estimate is accurate because the data shows that 240 employees will ask for time off. 5

Lesson Quiz for Student Response Systems 3. A machine produces 225,000 insulating washers for electrical devices per day. In a random sample of 200 washers, there were 4 defectives. Predict the number of defective washers produced by the machine per day. A. 2,250 B. 4,500 C. 9,000 D. 22,500 6