1. Which of the following are continuous random variables? (select all that apply)
a. The distance a person has walked in a day
b. How many glasses of water a person consumes in a day
c. The number of steps a person has walked in a day
d. The time it takes someone to tie their shoes
e. The speed of a car on a Phoenix freeway during rush hour traffic
2. Which of the following variable(s) would be considered a discrete random variable? (Select all that apply)
a. The number of students who bring their lunch to school instead of eating what the cafeteria serves.
b. The number races a race car driver competes in during a given year.
c. The average speed of a race car during a given race.
d. The time it takes a student to finish his/her lunch.
e. The cost of a statistics textbook
1. a, b, d, e ?
2. a, b, e ?
looks good to me
1. Hey there! Let's see which variables are continuous random variables:
a. The distance a person has walked in a day - Yup, that's continuous! They could walk any distance.
b. How many glasses of water a person consumes in a day - Hmm, this one is actually discrete. They can only consume a whole number of glasses, right?
c. The number of steps a person has walked in a day - Similar to b, this one is also discrete. It can only be a whole number of steps.
d. The time it takes someone to tie their shoes - You got it, this one is continuous! It can take any amount of time.
e. The speed of a car on a Phoenix freeway during rush hour traffic - Absolutely, this is continuous! The speed can vary continuously.
So the correct answers are: a, d, e.
2. Now let's find the random variables that are discrete:
a. The number of students who bring their lunch to school instead of eating what the cafeteria serves - Exactly, this one is discrete! It can only be a whole number.
b. The number of races a race car driver competes in during a given year - Bingo, this one is also discrete! They can only compete in a whole number of races.
c. The average speed of a race car during a given race - This one is actually continuous. The average speed can be any value.
d. The time it takes a student to finish his/her lunch - Good observation, this one is usually continuous. It can take any amount of time, even fractions of a minute.
e. The cost of a statistics textbook - You're right, this one is discrete! The cost is usually expressed as a specific dollar amount.
So the correct answers are: a, b, e.
Thanks for clowning around with me! Let me know if you have any more questions.
1. The correct options for continuous random variables are:
a. The distance a person has walked in a day
e. The speed of a car on a Phoenix freeway during rush hour traffic
2. The correct options for discrete random variables are:
a. The number of students who bring their lunch to school instead of eating what the cafeteria serves.
b. The number races a race car driver competes in during a given year.
e. The cost of a statistics textbook
1. To determine which of the given variables are continuous random variables, we need to understand the definition of a continuous random variable.
A continuous random variable is one that can take any value within a given range or interval. It can take on an infinite number of possible values, including decimal values.
a. The distance a person has walked in a day: This is a continuous random variable because it can take any value within a range (e.g., 0.5 miles, 1.3 miles, 2.7 miles, etc.).
b. How many glasses of water a person consumes in a day: This is NOT a continuous random variable because it can only take discrete values (e.g., 0 glasses, 1 glass, 2 glasses, etc.). It is better classified as a discrete random variable.
c. The number of steps a person has walked in a day: This is NOT a continuous random variable because it can only take discrete values (e.g., 0 steps, 1 step, 2 steps, etc.). It is better classified as a discrete random variable.
d. The time it takes someone to tie their shoes: This is a continuous random variable because it can take any value within a range (e.g., 10 seconds, 12.5 seconds, 15 seconds, etc.).
e. The speed of a car on a Phoenix freeway during rush hour traffic: This is a continuous random variable because it can take any value within a range (e.g., 55 mph, 60.2 mph, 65.8 mph, etc.).
Therefore, the continuous random variables in this case are: a (The distance a person has walked in a day), d (The time it takes someone to tie their shoes), and e (The speed of a car on a Phoenix freeway during rush hour traffic).
2. To determine which of the given variables are discrete random variables, we again need to understand the definition of a discrete random variable.
A discrete random variable is one that can only take on a finite or countable number of possible values.
a. The number of students who bring their lunch to school instead of eating what the cafeteria serves: This is a discrete random variable because it can only take a finite number of values (e.g., 0 students, 1 student, 2 students, etc.).
b. The number races a race car driver competes in during a given year: This is a discrete random variable because it can only take a countable number of values (e.g., 0 races, 1 race, 2 races, etc.).
c. The average speed of a race car during a given race: This is NOT a discrete random variable because it can take any value within a range (e.g., 150 mph, 152.5 mph, 155.8 mph, etc.). It is better classified as a continuous random variable.
d. The time it takes a student to finish his/her lunch: This is NOT a discrete random variable because it can take any value within a range (e.g., 10 minutes, 12.5 minutes, 15 minutes, etc.). It is better classified as a continuous random variable.
e. The cost of a statistics textbook: This is a discrete random variable because it can only take a finite number of values (e.g., $50, $75, $100, etc.).
Therefore, the discrete random variables in this case are: a (The number of students who bring their lunch to school instead of eating what the cafeteria serves), b (The number races a race car driver competes in during a given year), and e (The cost of a statistics textbook).
So, the correct answers are:
1. The continuous random variables are: a (The distance a person has walked in a day), d (The time it takes someone to tie their shoes), and e (The speed of a car on a Phoenix freeway during rush hour traffic).
2. The discrete random variables are: a (The number of students who bring their lunch to school instead of eating what the cafeteria serves), b (The number races a race car driver competes in during a given year), and e (The cost of a statistics textbook).