QMB 3200 TEST #1 QUESTIONS AND ANSWERS 2024

Discrete Data Values are whole numbers (integers) -Usually counted, not measured Continuous Data Can potentially take on any value, depending only on the ability to measure accurately -Often measured, fractional values are possible Discrete Random Variables have outcomes that typically take on whole numbers as a result of conducting an experiment Continuous Random Variables have outcomes that take on any numerical value as a result of conducting an experiment or -outcome that take on any numerical value in an interval probabilities are based on intervals, not individual values, also represented by an area Discrete Random Variables are? A FINITE number of values Continuous Random Variables are? A INFINITE number of outcomes Discrete Probability Distribution a listing of all the possible outcomes of an experiment for a discrete random variable Relative Frequency Probability Rules of Discrete Probability Distribution Must meet each of the following conditions: -each outcome in the distribution needs to be mutually exclusive with other outcomes in the distributions -the probability of each outcome, P(x), must be between 0 and 1 (inclusive) -the sum of the probabilities for a ll the outcomes in the distribution must be 1 The Mean (mew) weighted average of the outcomes of the random variables that comprise it Another Way to Say Expected Value? E(x) mean or average Variance is a measure of the spread of the individual values around the mean of a data set Standard Deviation is the square root of the variance Expected Monetary Value is the mean of a discrete probability distribution when the discrete random variable is expressed in terms of dollars -represents a long term average What is a Binomial Distribution? -A specific type of discrete probability distribution -is used to calculate the probability of a specific number of successes (x) for a certain number of trials (n), given specified probability of success (p) and probability of failure (q) Characteristics of a Binomial Experiment? -the experiment consists of a fixed number of trials, denoted by n -each trial has only two possible outcomes, a success and failure -the probability of a success, p, and failure, q, are constant through out the experiment -each trial is independent of the other trials in the experiment What are the 3 Types of Continuous Probability Distributions? Normal Probability Distribution Exponential Distribution Uniform Distribution Exponential Distribution is used to describe data where lower values tend to dominate and higher values don't occur very often Uniform Distribution describes data where all the values have the same chance of occuring Characteristics of the Normal Probability Distribution -bell shaped -symmetrical around the mean - the total area under the curve is always equal to 1 In a Normal Probability Distribution what are the mean and median value? And why? The mean and median value are the same value, because the distribution is symmetrical The changing of the Mean in a Normal Distribution does what to the shape? Shifts the distributions the left or the right The changing of the Standard Deviation in a Normal Distribution does what to the shape? Increases of decreases the spread (tall or flat) Probability Density Function is a mathematical description of a probability distribution -describes the shape of the normal probability distribution -represents the relative distribution of frequency of a continuous random variable Standard Normal Distribution Turning x-units into z- units, or a z-score -and normal distribution (with any mean and standard deviation combination) can be transformed into a z-score z-score lets you look up probability quickly (find probability under the curve) -mean of z = 0 -standard deviation of z = 1 What does a Negative Z-score mean? What does a Positive Z-score mean? -values of x that are less than the distribution mean -values of x that are more than the distribution mean What is the Empirical Rule? -stating that for a normal distribution, almost all data will fall within three standard deviations from the mean 68%, 95%, 99.7% To get the the probability of two values (interval) in a Normal Distribution what do you do? -anytime you have an interval to get probability between subtract low (small) z from the large (high) z When can you use the normal distribution as an approximation to the Binomial Distribution? - can be used when the sample size is large enough so the