What is a sample and how does it differ from a population? Provide an example of each concept. A population and a sample have different meanings in statistics. A population means the entire information under a statistical inquiry. It is the entire set of observations of a study obtained through complete enumeration or census (Waclawski, & Church, 2002). The population is sometimes called the universe. A sample means a portion of the population that is selected for a given statistical inquiry. It is drawn from the parent population and has properties similar to those of the parent population. Therefore, a sample statistic gives an estimate of the population parameter (Di Pofi, 2002). To achieve this, it must be representative of the population in property and character; it must give an accurate picture of the parent population so that the corresponding properties of the whole observations can be estimated accurately. For example, to find out the opinion of American citizens about the firearm policy in the U.S., the population would be the entire United States citizens. A sample of 1000 people can be drawn randomly from different states to represent the population. The sample must be random and representative to avoid selection bias. Describe the basic characteristics of a normal distribution and the normal curve. What is the usefulness of the normal distribution and its applications in statistics? The normal distribution is an important type of theoretical distribution. Unlike other theoretical distributions such as Poisson and Binomial distributions that are discreet, the normal distribution is a continuous probability distribution (Di Pofi, 2002). It is often known as a Gaussian distribution after F. Gauss who first studied and derived the normal distribution equation. The normal curve is a symmetrical curve that runs indefinitely in either direction of the horizontal axis but does not touch it (Di Pofi, 2002). The normal distribution is expressed as N (µ, σ), with µ representing the mean and σ representing the deviation (SD) about the mean. Varying values of µ and σ means that a normal distribution can take different shapes. The probability distribution, p (x), of a variable in a normal distribution is determined by the area under the normal curve. The normal curve encloses an area that has a probability of 1. The normal distribution has several basic properties; first, its mean, mode, and median are all equal. The normal distribution also has only one mode. It is symmetrical about the µ; the two halves about the µ mirror each other (Di Pofi, 2002). Also, the area under the curve, which is 1, is divided into 0.5 to the right and left of the mean value of a normal distribution. At the µ value, the curve is concave, at ±σ, it curves inwards forming the points of inflection and at ±3σ the curve becomes convex relative to the x-axis. The normal distribution has many applications in practice. Most sampling distributions including Z- distribution, F -test, and t -test involve normal distribution for large values of n (n→∞). Also, calculations involving test statistics such as F- test and student’s t -test are based on the assumption that the parent population is normally distributed (Di Pofi, 2002). The normal distribu