Lesson 9: Practice Problems

Problem 1

Suppose 45% of all the students at Andre’s school brought in a can of food to contribute to a canned food drive. Andre picks a representative sample of 25 students from the school and determines the sample’s percentage.

He expects the percentage for this sample will be 45%. Do you agree? Explain your reasoning.

Problem 2

This is a dot plot of the scores on a video game for a population of 50 teenagers.

A dot plot for “score on a video game.” The numbers 40 through 200, in increments of 10, are indicated. The data are as follows: Score of 40, 1 dot. Score of 45, 1 dot. Score of 60, 1 dot. Score of 65, 2 dots. Score of 70, 2 dots. Score of 75, 2 dots. Score of 80, 2 dots. Score of 85, 2 dots. Score of 90, 2 dots. Score of 95, 2 dots. Score of 100, 2 dots. Score of 105, 1 dot. Score of 110, 2 dots. Score of 115, 2 dots. Score of 120, 3 dots. Score of 125, 3 dots. Score of 130, 5 dots. Score of 135, 2 dots. Score of 145, 1 dot. Score of 150, 1 dot. Score of 155, 1 dot. Score of 160, 1 dot. Score of 170, 2 dots. Score of 175, 2 dots. Score of 180, 1 dot. Score of 190, 2 dots. Score of 195, 1 dot. Score of 200, 1 dot.

The three dot plots together are the scores of teenagers in three samples from this population. Which of the three samples is most representative of the population? Explain how you know.

Three dot plots for “score on a video game” are labeled “sample 1,” “sample 2,” and “sample 3.” The numbers 40 through 200, in increments of 10, are indicated. The data are as follows: Sample 1: Score of 75, 2 dots. Score of 100, 1 dot. Score of 110, 1 dot. Score of 130, 1 dot. Score of 160, 1 dot. Score of 170, 2 dots. Score of 180, 1 dot. Score of 195, 1 dot. Sample 2: Score of 160, 1 dot. Score of 170, 2 dots. Score of 175, 2 dots. Score of 180, 1 dot. Score of 190, 2 dots. Score of 195, 1 dot. Score of 200, 1 dot. Sample 3: Score of 40, 1 dot. Score of 45, 1 dot. Score of 60, 1 dot. Score of 70, 2 dots. Score of 80, 1 dot. Score of 100, 2 dots. Score of 105, 1 dot. Score of 115, 1 dot.

Problem 3

This is a dot plot of the number of text messages sent one day for a sample of the students at a local high school. The sample consisted of 30 students and was selected to be representative of the population.

A dot plot for “number of text messages sent.” The numbers 0 through 90, in increments of 5, are indicated. The data are as follows: 0 text messages, 6 dots. 2 text messages, 2 dots. 8 text messages, 3 dots. 10 text messages, 2 dots. 11 text messages, 1 dot. 13 text messages, 1 dot. 14 text messages, 1 dot. 16 text messages, 1 dot. 17 text messages, 1 dot. 20 text messages, 1 dot. 23 text messages, 1 dot. 24 text messages, 1 dot. 26 text messages, 1 dot. 30 text messages, 1 dot. 31 text messages, 2 dots. 32 text messages, 1 dot. 35 text messages, 1 dot. 41 text messages, 1 dot. 75 text messages, 1 dot. 90 text messages, 1 dot.

What do the five values of 0 in the dot plot represent?
Since this sample is representative of the population, describe what you think a dot plot for the entire population might look like.

Problem 4 From Unit 8 Lesson 8

A doctor suspects you might have a certain strain of flu and wants to test your blood for the presence of markers for this strain of virus. Why would it be good for the doctor to take a sample of your blood rather than use the population?