Predicting from Random Samples

In a survey, 45 out of a random sample of 150 people said they prefer tea over coffee. Predict how many people would prefer tea in a city of 30,000 people.

• 9000

• 15000

• 4500

• 12000

Answer explanation

Since 45 out of 150 prefer tea, the ratio is 45/150. Applying this ratio to 30,000 people gives 9000 people who would prefer tea.

A study on a random sample of 250 cars passing through a toll booth shows that 75 cars are from out of state. Predict the number of out-of-state cars among 1000 cars passing through the toll booth.

• 300

• 250

• 200

• 350

Answer explanation

To predict the number of out-of-state cars among 1000 cars, use the ratio from the sample: 75/250 = x/1000. Solving for x gives 300.

In a random sample of 60 apples from a farm, 12 apples were found to be rotten. If the farm has 3000 apples, predict the number of rotten apples.

• 600

• 240

• 120

• 480

Answer explanation

To predict the number of rotten apples, use the ratio of rotten apples in the sample to the total apples in the farm: (12/60) * 3000 = 240 rotten apples.

Tags

CCSS.7.RP.A.3

A random sample of 100 voters from a small town shows that 55 voters support candidate A. If the town has 2000 voters, how many voters are likely to support candidate A?

• 1100

• 1000

• 900

• 1200

Answer explanation

To find the number of voters supporting candidate A in the town, we can use the ratio of voters in the sample to the total voters. 55/100 = x/2000. Solving for x gives us 1100 voters likely to support candidate A.

Tags

CCSS.7.RP.A.3

In a random sample of 40 pieces of candy, 10 pieces are sour. Predict how many pieces will be sour if there are 200 pieces of candy.

• 50

• 40

• 60

• 30

Answer explanation

Since 10 out of 40 pieces are sour, the proportion is 10/40 = 1/4. Applying the same ratio to 200 pieces gives 1/4 * 200 = 50 sour pieces.

Tags

CCSS.6.RP.A.3B

A survey on a random sample of 500 people in a city shows that 250 people use public transportation. Predict the number of people using public transportation if the city's population is 10,000.

• 5000

• 2500

• 7500

• 1000

Answer explanation

To predict the number of people using public transportation in a city with a population of 10,000, we can use the ratio from the sample. 250 people out of 500 use public transportation, so in a population of 10,000, we can expect 5000 people to use public transportation.

Tags

CCSS.7.RP.A.3

In a random sample of 20 students from a class, 8 students said they participate in after-school sports. Predict the total number of students participating in after-school sports in a school of 400 students.

• 160

• 80

• 120

• 200

Answer explanation

To find the total number of students participating in after-school sports in a school of 400 students, we can use the ratio method. 8 students out of 20 participate, so 8/20 = x/400. Solving for x gives us 160 students.

Tags

CCSS.7.RP.A.3

A random sample of 150 houses in a neighborhood shows that 45 houses have a swimming pool. If there are 750 houses in the neighborhood, how many houses are likely to have a swimming pool?

• 225

• 150

• 300

• 275

Answer explanation

To find the number of houses likely to have a swimming pool, we can use the ratio of houses with a pool in the sample to the total number of houses in the neighborhood: (45/150) * 750 = 225.

Tags

CCSS.7.RP.A.3

In a random sample of 30 cookies, 9 cookies have chocolate chips. Predict how many cookies will have chocolate chips if 150 cookies are made.

• 45

• 30

• 60

• 75

Answer explanation

Since 9 out of 30 cookies have chocolate chips, the proportion is 9/30. Applying this proportion to 150 cookies gives 45 cookies with chocolate chips.

Tags

CCSS.7.RP.A.3

A random sample of 200 people at a concert shows that 120 people are wearing hats. Predict the number of people wearing hats if 800 people are at the concert.

• 480

• 320

• 600

• 400

Answer explanation

To predict the number of people wearing hats for 800 attendees, use the ratio of people wearing hats in the sample. 120/200 = x/800. Solving for x gives 480.

Tags

CCSS.7.RP.A.3