STAT 210 1st EditionExam 4 Study Guide Lectures 17-20Lecture 17 (Oct 7th) What are the characteristics of a normal distribution?- Normal curve is bell shaped- Peak of the curve is population mean - Normal curve is symmetric about - Center and spread are completely specified by specifying the values of the population mean  and standard deviation - Total area under normal curve is 1 or 100%Explain the 68-96-99.7% rule- It means 68% fall within one standard deviation, 95% fall within one standard deviation, or 99.7% fall within one standard deviationWhat does a normal table do? - Gives the probability that the standard normal variable Z falls below some specified valueLecture 18 (Oct 9th) How to solve a greater than problem?- Just change it to a less than problem: - P(Z > z) = 1  1-P(Z <z)How to solve a less than problem?- Draw a normal curve and mark the information stated in the problem- In the normal table find the specified less that probability in the body of the tableand then read across and up to determine the appropriate z valueHow to solve a between problem?- Find the two values such that the probability of being between the two values is .60- Since the probability of being between the two values is .60, then the total probability outside (les than z1 and greater than z2) is 1-.60 = .40Lecture 19 (Oct 11th) Notation of a Z-score transformation- Z ~ N(0,1)- Z = (x – /) = (value – mean/standard deviation) Characteristics of a standard normal distribution- Denoted by Z, has population mean  = 0 (center), has population standard deviation = 1 (spread), shape is normal (symmetrical bell curve), no unusual features, Z ~ N(0,1)Lecture 20 (Oct 14th) Characteristics of a student’s t-distribution- The Z-distribution and all t-distributions have the same symmetric, bell-shape - The Z-distribution and all t-distributions have the same mean, which is 0.- The standard deviation of the Z-distribution is 1, but the standard deviation of a t-distribution will be greater than or equal to 1 and depends on what is called thedegrees of freedom (denoted df). As the degrees of freedom increases, the t-distribution gets closer and closer to the Z-distribution to the point that for df = ∞ the Z and t-distributions are the same and the standard deviation of the t-distribution with df = ∞ is 1 (the same as for Z). - The Z-distribution and all t-distributions have the same symmetric, bell-shape, and therefore none of the distributions have any unusual features.What is a sampling distribution?- A sampling distribution of a statistic is the distribution of values taken by the statistic in a large number of simple random samples of the same size n taken from the same