1. Predicting from Samples

2. 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

3. Additional Example 3 Continued
6 25 x
Let x represent the number of actual students attending the band festival. =
6 • 1500 = 25 • x
The cross products are equal.
9000 = 25x
Multiply.
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

4. 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

5. Check It Out: Example 3 Continued
8 40 x
Let x represent the number of actual employees asking for time off. =
8 • 1200 = 40 • x
The cross products are equal.
9600 = 40x
Multiply.
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

6. 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