Section 5.6: Normal as Approximation to Binomial

1. Use Triola & Triola’s rule of thumb to determine when the normal distribution approximation to the binomial distribution is appropriate.
2. Determine the appropriate mean and standard deviation for the normal distribution approximating a binomial distribution with \(n\) trials and success probability \(p\).
3. Explain why, in terms of the probability histogram for a binomial distribution, the continuity correction is desirable when computing binomial probabilities using the normal density histogram. You will not need to use the continuity correction on homework and exams.
4. For a binomial random variable \(X\) with \(n\) trials and success probability \(p\), use the normal distribution approximation to the binomial distribution to compute binomial probabilities such as \(P(X \leq x)\), \(P(X < x)\), \(P(X \geq x)\), \(P(X > x)\), and \(P(X = x)\).

Section 7.3: Testing a Claim About a Proportion

1. Recognize the notation \(p\) for the population proportion and \(\widehat{p}\) for the sample proportion.
2. State the appropriate null and alternative hypotheses when given a claim about a population proportion.
3. State the \(Z\) test statistic for a population proportion.
4. Test a claim about a population proportion \(p\) using the appropriate \(Z\) test statistic for the population proportion using:
   • The Traditional Method, using a rejection region
   • The \(P\)-value Method
5. State when a hypothesis test for the population proportion \(p\) using the \(Z\) test statistic is appropriate.
6. State the margin of error for a population proportion \(p\) when we use the normal distribution approximation to the binomial distribution.
7. Construct a confidence interval for the population proportion \(p\) using the normal distribution approximation to the binomial distribution.