#### Solved Examples and Worksheet for Making Predictions

Q1While inspecting 500 compact disks, Chris found that 20 of them were defective. How many defective disks can he expect in a sample of 2000 disks?

A. 180
B. 80
C. 90
D. None of the above

Step: 1
Let x be the number of defective disks.
Step: 2
(Number of defective compact disks in the sample) / (Total number of disks in the sample) = (Number of defective disks in a sample of 2000 disks) / (Total number of disks)
Step: 3
20500 = x2000
[Write a proportion.]
Step: 4
x = 20 × 2000500
[Write the cross products.]
Step: 5
= 80
[Simplify.]
Step: 6
Chris can expect 80 disks to be defective in a sample of 2000 disks.
Q2From a sample of 150 doorbells, if 6 are defective, predict the number of defective doorbells in a sample of 15,000 doorbells.

A. 600
B. 100
C. 1000
D. 150

Step: 1
Let the number of doorbells defective in a sample of 15,000 doorbells be y.
Step: 2
Doorbells defective in a sample of 150 doorbells / Number of doorbells = Doorbells defective in a sample of 15,000 doorbells / Number of doorbells
Step: 3
6150 = y15000
[Write the proportion.]
Step: 4
y = 6 × 15000150
[Write the cross products.]
Step: 5
= 600
[Simplify.]
Step: 6
Number of doorbells defective in a sample of 15,000 is 600.
Q3A shoe manufacturer finds 10 pairs of defective shoes while inspecting a sample of 50 pairs. Predict the number of defective pairs from a total number of 250 pairs of shoes.

A. 50
B. 12
C. 10
D. 25

Step: 1
Let y be the number of pairs defective out of 250 pairs.
Step: 2
Number of pairs defective in 50Number of sample pairs = Number of pairs defective in 250Total number of pairs
Step: 3
1050 = y250
[Substitute.]
Step: 4
y = 10 × 25050
[Write the cross products.]
Step: 5
= 50
[Simplify.]
Step: 6
The shoe manufacturer can predict 50 pairs of defective shoes.
Q4The circle graph shows the favorite sports of the students of the Earl High School. Find the number of students who like football if there are 2500 students. A. 800
B. 850
C. 900
D. None of the above

Step: 1
Let y be the number of students who like football out of 2500.
Step: 2
Write a proportion.
Step: 3
34100 = y2500
[Substitute.]
Step: 4
y = 2500 × 34100
[Write the cross products.]
Step: 5
= 850
[Multiply.]
Step: 6
850 out of 2500 students like football.
Q5Using the graph, find the distance Justin covers in 20 hours. A. Greater than 250 mi
B. Greater than 100 mi
C. Greater than 200 mi
D. Greater than 150 mi

Step: 1
From the graph, the distance that Justin covers is increasing in each hour.
Step: 2
The distance that Justin covers in 15 hours is 150 mi.
Step: 3
So, one would expect the distance that Justin covers in 20 hours to be certainly greater than 150 mi.
Correct Answer is :   Greater than 150 mi
Q6A pie chart is drawn to show the results of a survey done on a sample of 100 people who like various sports. Find the number of people who like wrestling out of a population of 2000. A. 500
B. 420
C. 460
D. None of the above

Step: 1
Let y be the number of people who like wrestling out of 2000.
Step: 2
Number of people who like wrestling out of 100 people / Total number of people = Number of people who like wrestling out of 2000 people / Total number of people
Step: 3
= 23100 = y2000
[Substitute.]
Step: 4
y = (23 × 2000)100
[Write the cross products.]
Step: 5
= 460
[Simplify.]
Step: 6
460 out of a population of 2000 people like wrestling.
Q7A pie chart is drawn to represent the survey done on a sample of 100 people who like various sports. Find the number of people who like football out of a population of 1000 people. A. 320
B. 360
C. 340
D. None of the above

Step: 1
Let y be the number of people who like football out of 1000.
Step: 2
Number of people who like football out of 100 people / Total number of people = Number of people who like football out of 1000 people / Total number of people
Step: 3
= 34100 = y1000
[Substitute.]
Step: 4
y = (1000 × 34)100
[Write the cross products.]
Step: 5
= 340
[Multiply.]
Step: 6
340 out of a population of 1000 people like football.
Q8A survey at Kennedy Middle School found that 8 of every 15 students prefer dance class to music class. If there are 600 students at the school, how many of them would you expect to prefer dance class to music class?
A. 420
B. 40
C. 300
D. 320

Step: 1
Let x be the number of students in the entire school who prefer dance class to music class.
Step: 2
Total number of students in the school = 600
Step: 3
815 = x600 x = 815 × 600 = 320
Step: 4
So, 320 students in the school prefer dance class to music class.
Q9The profit (in percent) of a company in the last 3 years is shown in the graph. Predict the profit of the company in the year 2005. A. 60 %
B. 40 %
C. 55 %
D. 50 %

Step: 1
Prediction means telling what would happen in the near future.
Step: 2
The graph shows an increasing trend in the profit earned by a company (in percent) during the last three years by 10% .
Step: 3
The profit earned by the company (in percent) in the year 2004 is 50%
Step: 4
So, it can be predicted that the profit earned by the company(in percent) for the year 2005 would be 60% .
Correct Answer is :   60 %
Q10The graph shows the monthly sales at Christina's grocery store. Predict the sales in June. A. more than $1,000 B. less than$1,000
C. more than $2,000 D. less than$10,000

Step: 1
The sales have been decreasing each month.
Step: 2
Sales in the month of May are $1,000. Step: 3 So, one would expect the sales in June to be less than$1,000.
Correct Answer is :   less than \$1,000
Q11The bar graph shows the population of a country (in millions). Predict the population of the country in 2003. A. more than 300 million
D. less than 200 million

Step: 1
From the bar graph, the difference in the population of a country in succeeding years is 50%.
Step: 2
So, the population in the year 2003 would be about 260 million.
Q12The graph shows the circulation of a magazine (in thousands) in the year 2003. Predict the circulation of the magazine in the first quarter of 2004. B. less than 160,000
C. less than 100,000

Step: 1
The given graph shows the circulation of a magazine (in thousands) in the year 2004.
Step: 2
The circulation of the magazine in the first quarter of 2004 will be about 180, 000.
Q13Out of a random sample of 150 people, 75 said they preferred rock music. How many people out of 600 could be predicted to prefer rock music?
A. 450
B. 225
C. 300
D. 150

Step: 1
Among 150 people, 75 preferred rock music.
[Given]
Step: 2
That means half of the people preferred rock music.
[As 75 is half of 150.]
Step: 3
So, 300 people out of 600 could be predicted to prefer rock music.
[As 300 is half of the 600.]
Q14A toy factory randomly checked 500 toys and found that 10 were defective. If the factory ships a carton of 200 toys to a store, how many defective toys can be predicted to be in the shipment?
A. 8
B. 4
C. 2
D. 6

Step: 1
Number of Toys checked = 500.
Step: 2
Number of Toys found to have defective = 10.
Step: 3
Probability of a Toys to have defective out of 100 = 10500
Number of favourable eventsTotal number of possible outcomes
Step: 4
150
[Simplify]
Step: 5
Number of Toys to have defective out of 200 magazines = 200 × 150
Step: 6
= 4.
[Simplify]
Q15A clothing manufacturer produces 6,000 T-shirts per week. A random sample of 100 shirts is tested and 6 are found to have defects. What would be the best prediction of the number of T-shirts that have defects each week of the production?
A. 6
B. 36
C. 360
D. 42

Step: 1
Number of T-shirts manufactured every week = 6000.
Step: 2
Number of T-shirts checked = 100.
Step: 3
So, the probability of getting a defective T-shirt = 6100
[Number of favorable events Total number of possible outcomes.]
Step: 4
= 350
Step: 5
Therefore, the number of T-shirts that can have defects in each week of the production = 6000 × 350
[Simplify.]
Step: 6
= 360