Random Variables and Normal Distribution

What is a random variable?

• A random variable is a variable that can take on different values with certain probabilities in a given probability space.

• A random variable is a variable that can only take on integer values in a given probability space.

• A random variable is a variable that has a fixed value in a given probability space.

• A random variable is a variable that is determined by a random process.

Give an example of a discrete random variable.

• The temperature in degrees Celsius

• Number of heads obtained when flipping a coin 10 times

• The height of a person in centimeters

• Number of tails obtained when flipping a coin 10 times

Provide an example of a continuous random variable.

• Number of siblings

• Temperature of a room

• Height of a person

• Color of a car

What are the properties of a normal distribution?

• The properties of a normal distribution are symmetry, bell-shaped curve, equal mean, median, and mode, characterized by mean and standard deviation, and total area under the curve is equal to 1.

• The properties of a normal distribution are skewness, flat curve, equal mean, median, and mode, characterized by mean and range, and total area under the curve is equal to 0.

• The properties of a normal distribution are asymmetry, U-shaped curve, unequal mean, median, and mode, characterized by mean and standard deviation, and total area under the curve is equal to 1.

• The properties of a normal distribution are randomness, step-shaped curve, equal mean, median, and mode, characterized by mean and variance, and total area under the curve is equal to 0.

How do you calculate probabilities using z-scores?

• Use the t-distribution table to find the corresponding probability based on the z-score.

• Use the chi-square distribution table to find the corresponding probability based on the z-score.

• Use the standard normal distribution table to find the corresponding probability based on the z-score.

• Use the mean and standard deviation to calculate the probability directly.

True or False: A random variable can only take on discrete values.

• False

• Depends on the situation

• Sometimes

• True

True or False: A normal distribution is symmetric.

• Not always

• Sometimes

• True

• False

True or False: The area under a normal distribution curve represents probabilities.

• False

• True

• Sometimes

• Only for certain distributions

True or False: The z-score measures the number of standard deviations a value is from the mean.

• The z-score measures the range of a value

• True

• False

• The z-score measures the median of a value

True or False: The probability of an event occurring in a normal distribution can be negative.

• True

• Maybe

• False

• Sometimes