Statistics and Probability

1. In a sample survey, what is the primary purpose of random sampling?

• To ensure that all members of the population have an equal chance of being selected

• To ensure that the sample accurately reflects the characteristics of the population

• To reduce the amount of time and effort required to collect the data

• To make the results of the survey more precise and accurate

2. What is the standard deviation of a set of numbers?

• The average of the numbers

• The average of the absolute values of the numbers

• A measure of how spread out the numbers are

• The sum of the numbers

3. What is the expected value of a random variable?

• The average value of the variable over a large number of observations

• The most likely value of the variable

• The value of the variable that has the highest probability of occurring

• The sum of all possible values of the variable

4. In a normal distribution, what is the probability that a randomly selected observation will fall within one standard deviation of the mean?

• Approximately 68%

• Approximately 95%

• Approximately 99.7%

• Approximately 50%

5. Which of the following is an example of a continuous probability distribution?

• The number of heads flipped in 10 coin tosses

• The number of cars passing by a certain intersection in an hour

• The number of people in a room who are taller than 6 feet

• The number of dogs in a neighborhood

6. What is the difference between a sample and a population in statistics?

• A sample is a subset of a population

• A population is a subset of a sample

• A population is a larger group than a sample

• A sample is a larger group than a population

7. Which of the following is an example of a continuous probability distribution?

• The number of heads when flipping a coin three times

• The number of students in a classroom

• The height of individuals in a population

• The number of red cars in a parking lot

8. What is the expected value in a probability distribution?

• The most likely outcome

• The mean of the distribution

• The mode of the distribution

• The median of the distribution

9. What is a conditional probability?

• The probability of an event given that another event has occurred

• The probability of two events occurring at the same time

• The probability of an event occurring within a given time frame

• The probability of an event occurring in a certain location

10. What is the main difference between statistics and probability?

• Statistics is the study of collecting, analyzing, and interpreting data, while probability is the likelihood of an event occurring.

• Statistics is the study of random phenomena, while probability is the study of structured, organized data.

• Statistics is the study of systematic data, while probability is the study of subjective data.

• Statistics is the study of large data sets, while probability is the study of small data sets.