STAT 503 - Quiz 4 Solved 2023

Normal distribution - ANSWER-- Symmetrical distribution - Works well for data that is subject to variation from a lot of different factors -Values in the middle are most common while tail values are extreme and rare -Numeric, continuous variables -N ~ (mu, sigma) Standard normal distribution - ANSWER-A normal distribution with a mean of 0 and a standard deviation of 1. Binomial distribution - ANSWER-- describes the number of "successes" that occur in a fixed number of independent trials, each with two possible outcomes (proportions) - better for population level questions than individual level questions - X ~ Bin(n,p) The binomial distribution applies if: - ANSWER-1.The data consist of n identical trials 2.Each trial can have one of two possible, mutually exclusive outcomes 3.The trials are all independent of each other 4.Each of the n trials has the same probability of "success," p. When can we use the binomial distribution for individual units? - ANSWER-only if all units have similar "p" Examples of binomial variables - ANSWER-The number of "heads" in 7 coin flips. The number of individuals in a random sample of 30 people who have a particular allele of a given gene. The number of trees that set fruit in a given year, out of n trees sampled from an orchard. The proportion of randomly selected individuals still alive after a particular length of time. Properties of the binomial distribution - ANSWER-The shape of the binomial distribution depends on p and n. •At p=0.5, the distribution is symmetric. •For p0.5 it is right-skewed. •For p0.5, it is left-skewed. •At any given value of p, the skew is less pronounced for larger values of n. As n→∞, p_x (x)→Normal Poisson distribution - ANSWER-models the number of events that occur in a given sample unit; the number of events that occur in each sample unit, instead of the number of units that belong to a category.