Statistics: Simulations and Sampling Worksheet

Question 1

A school has 600 students. The principal wants to know which new lunch item students prefer. She surveys the first 30 students who enter the cafeteria on Monday. Explain whether this is likely to be a representative sample.

Accepted Answer

This is not likely to be a representative sample because the first 30 students who enter the cafeteria may not represent all students in the school. A better sample would randomly choose students from different grades and lunch times.

Question 2

A bag has 4 red marbles and 6 blue marbles. You want to simulate drawing one marble without looking. Which simulation tool could you use, and how would you set it up?

Accepted Answer

You could use a random number generator with numbers 1 through 10. Let 1 through 4 represent red marbles and 5 through 10 represent blue marbles.

Question 3

A survey of 50 randomly chosen students found that 18 students ride the bus to school. Estimate how many of the 800 students in the school ride the bus.

Accepted Answer

The sample proportion is 18 out of 50, or 0.36. The estimate is 0.36 times 800, so about 288 students ride the bus.

Question 4

A spinner has 5 equal sections: 2 green, 2 yellow, and 1 purple. Describe how to simulate one spin using slips of paper.

Accepted Answer

You could write green on 2 slips, yellow on 2 slips, and purple on 1 slip. Put all 5 slips in a cup, mix them, and draw one slip to represent one spin.

Question 5

A student wants to estimate the average number of books read by middle school students in a month. She only asks students in the library after school. Identify the sampling problem and suggest an improvement.

Accepted Answer

The sample may be biased because students in the library may read more books than other students. She should randomly sample students from different classes or grades.

Question 6

A basketball player makes about 70% of free throws. To simulate 20 free throws, you use random digits 0 through 9. Which digits could represent a made free throw, and which could represent a missed free throw?

Accepted Answer

Seven of the ten digits should represent a made free throw. For example, digits 0 through 6 can represent a make, and digits 7 through 9 can represent a miss.

Question 7

A random sample of 40 households in a town shows that 12 households have a vegetable garden. Estimate how many of the 2,500 households in the town have a vegetable garden.

Accepted Answer

The sample proportion is 12 out of 40, or 0.30. The estimate is 0.30 times 2,500, so about 750 households have a vegetable garden.

Question 8

The table shows results from a simulation of rolling a number cube 60 times: 1 appeared 8 times, 2 appeared 12 times, 3 appeared 9 times, 4 appeared 11 times, 5 appeared 10 times, and 6 appeared 10 times. Based on the simulation, what is the experimental probability of rolling a 2?

Accepted Answer

The experimental probability of rolling a 2 is 12 out of 60, which simplifies to 1 out of 5 or 0.20.

Question 9

A company wants to know if customers like a new package design. They ask only customers who already gave the product a 5-star review. Explain why this sample may be biased.

Accepted Answer

This sample may be biased because it only includes customers who already liked the product very much. Their opinions may not represent all customers.

Question 10

You need to simulate whether a randomly chosen day is a weekend or a weekday. Describe a fair simulation using numbers 1 through 7.

Accepted Answer

You could let numbers 1 through 5 represent weekdays and numbers 6 and 7 represent weekend days. Randomly choosing one number from 1 through 7 would simulate one randomly chosen day.

Question 11

A sample of 100 randomly selected voters shows that 56 plan to vote yes on a proposal. Estimate how many of the 12,000 voters in the city plan to vote yes.

Accepted Answer

The sample proportion is 56 out of 100, or 0.56. The estimate is 0.56 times 12,000, so about 6,720 voters plan to vote yes.

Question 12

The dot plot shows the number of pets owned by 20 randomly selected students. Most values are 0, 1, or 2, with one value at 7. Explain how the value 7 might affect the mean compared with the median.

Accepted Answer

The value 7 is much larger than the other values, so it can pull the mean upward. The median is less affected because it depends on the middle values, not the size of the largest value.

Question 13

A jar has an unknown mix of red and white counters. In a simulation of 80 draws with replacement, red was drawn 30 times. Estimate the probability of drawing a red counter.

Accepted Answer

The estimated probability of drawing a red counter is 30 out of 80, which is 0.375 or 37.5%.

Question 14

A teacher wants a random sample of 25 students from a school of 500 students. Describe a method that gives every student an equal chance of being selected.

Accepted Answer

The teacher could assign each student a number from 1 to 500 and use a random number generator to choose 25 different numbers. The students with those numbers would be selected.

Question 15

Two students run simulations to estimate the probability of getting heads when flipping a fair coin. Student A flips 10 times and gets heads 8 times. Student B flips 200 times and gets heads 104 times. Which result is likely to be closer to the true probability, and why?

Accepted Answer

Student B's result is likely to be closer to the true probability because it uses many more trials. Larger numbers of trials usually give experimental probabilities that are closer to the theoretical probability.

Statistics: Simulations and Sampling

Related Cheat Sheets

More Statistics Worksheets

More Grade 6-8 Worksheets