PRETEST - Statistics and Probability

What is a random variable?

• A random variable is a variable that only takes on values from a specific set of outcomes.

• A random variable is a constant that represents a specific event in a process.

• A random variable is a fixed number that does not change.

• A random variable is a variable that takes on numerical values determined by the outcomes of a random process.

Define the sample space in a probability experiment.

• The sample space is the most likely outcome of an experiment.

• The sample space is the average of all outcomes.

• The sample space is the set of all possible outcomes of a probability experiment.

• The sample space is the sum of all possible outcomes.

The following are example of a continuous variable except:

• Students in a Classroom

• Weight of students

• Height of buildings

• Temperature of a child

What distinguishes a discrete variable from a continuous variable?

• Discrete variables are always integers; continuous variables are always decimals.

• Discrete variables can take any value; continuous variables can only take whole numbers.

• Discrete variables are measurable; continuous variables are countable.

• Discrete variables are countable; continuous variables are measurable.

Explain what a probability distribution is.

• A probability distribution is a fixed set of outcomes that cannot change.

• A probability distribution is a method to calculate the average of a dataset.

• A probability distribution is a graphical representation of data points.

• A probability distribution is a function that describes the likelihood of different outcomes for a random variable.

What is the shape of a normal curve?

• Triangular and uneven.

• Circular and distorted.

• Bell-shaped and symmetric.

• Square and flat.

How do you calculate the mean of a discrete random variable?

• Mean = Σ (x * P(x))

• Mean = Σ (x + P(x))

• Mean = P(x) * x^2

• Mean = Σ (P(x) / x)

What is the significance of the standard deviation in a normal distribution?

• The standard deviation indicates the spread of data points around the mean in a normal distribution.

• The standard deviation indicates the maximum value in a normal distribution.

• The standard deviation measures the total number of data points in a distribution.

• The standard deviation is the average of all data points in a normal distribution.

Describe the Central Limit Theorem in relation to sample means.

• The Central Limit Theorem states that the distribution of sample means approaches a normal distribution as the sample size increases.

• Sample means will always be normally distributed regardless of sample size.

• The Central Limit Theorem applies only to populations with a normal distribution.

• The Central Limit Theorem states that sample means are always equal to the population mean.

How can you determine if a variable follows a normal distribution?

• Check if the variable is a string.

• Use only the mean and median values.

• Assume all data is normally distributed without testing.

• Use visual methods and statistical tests to assess normality.