Statistics and Probability Quiz

What does the mean of a discrete random variable represent?

• The spread of the outcomes

• The highest outcome in the distribution

• The average value of the outcomes

• The lowest outcome in the distribution

How is the variance of a probability distribution calculated?

• By summing the outcomes

• By summing the squared differences between each outcome and the mean, multiplied by their respective probabilities

• By finding the median of the distribution

• By finding the mode of the distribution

In a normal random variable, what determines the spread of the distribution?

• The mean

• The median

• The variance

• The mode

Which of the following statements is true about the normal distribution?

• It is always skewed to the left.

• It has a mean of 0 and a variance of 1.

• Approximately 50% of the data falls within one standard deviation of the mean.

• It is not symmetric around its mean.

What percentage of data falls within one standard deviation of the mean in a normal distribution, according to the empirical rule?

• 50%

• 68%

• 95%

• 99.7%

What does the variance of a discrete random variable signify?

• The average of all outcomes

• The spread or dispersion of the outcomes around the mean

• The highest outcome in the distribution

• The lowest outcome in the distribution

How is the mean of a probability distribution calculated?

• By summing the outcomes

• By summing the squared differences between each outcome and the mean, multiplied by their respective probabilities

• By finding the median of the distribution

• By finding the mode of the distribution

In a normal random variable, which parameter determines the center of the distribution?

• The mean

• The median

• The standard deviation

• The mode

Which of the following statements about the normal distribution is correct?

• It is always positively skewed.

• It has a mean of 1 and a standard deviation of 0.

• It is not symmetric around its mean.

• It is bell-shaped and symmetric around its mean.

According to the empirical rule, what percentage of data falls within two standard deviations of the mean in a normal distribution?

• 25.13%

• 50.14%

• 68.26%

• 95.44%