Section 4.4: Mean, Variance, and Standard Deviation of the Binomial Distribution

1. Compute the mean, variance, and standard deviation of a binomial random variable with parameters \(n\) and \(p\).
2. Use the range / standard deviation rule-of-thumb to identify usual and unusual numbers of successes for a binomial random variable with parameters \(n\) and \(p\).
3. Explain the interpretation of the mean of a binomial random variable under the frequency interpretation of probability.
4. Construct a probability histogram for a binomial random variable \(X\) given the probability distribution of \(X\).

Section 5.1: Overview

1. Compare and contrast density histograms and frequency histograms.
2. State the properties that must be true of the graph of a function for it to be the graph of a density histogram.
3. Relate the area under a density histogram between \(x = a\) and \(x = b\) to the probability that a random variable \(X\) following that density histogram falls in the interval \([a, b]\).

Section 5.2: The Standard Normal Distribution

1. Sketch the graph of the density histogram for a standard normal random variable.
2. Relate the mean and standard deviation of a density histogram to the mean and standard deviation of a frequency histogram.
3. Specify the mean and standard deviation of a standard normal random variable.
4. Use a table like Table A–2 in Triola and Triola to find \(P(Z \leq z)\) for a standard normal random variable \(Z\).
5. Reason from a sketch of the density histogram of a standard normal random variable to identify \(P(Z \leq z)\), \(P(Z \geq z)\), and \(P(a \leq Z \leq b)\) for a random variable \(Z\).
6. Use a table like Table A–2 in Triola and Triola to find \(P(Z \leq z)\), \(P(Z \geq z)\), and \(P(a \leq Z \leq b)\) for a standard normal random variable \(Z\).
7. Use a table like Table A–2 in Triola and Triola to find the \(z\)-values (“\(z\)-scores”) that make the equality \(P(Z \leq z) = p\) true for given value of \(p\) for a standard normal random variable \(Z\).