STAT 301 Lecture Notes - Normal Distribution, Random Variable
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This is a particular normal distribution that has mean = 0 and variance 2 = 1, denoted. A variable that follows a standard normal distribution is usually denoted z. Areas for the standard normal distribution are listed in table 2 of appendix b, and in back cover (will post on ramct) Say that we want to find the probability that a random variable z is smaller than some number z*, i. e. , p(z z*) So we want to find p(z 1. 86) P(z 1. 86) = 1 p(z 1. 86) = 0. 0314. If we want to find p(-1. 86 < z < 1. 86) P(-1. 86 < z < 1. 86) = p(z < 1. 86) p(z < -1. 86) Say we want to find z* such that p(z < z*) = . 975 (want to find the 97. 5th percentile) Find . 975 in probability area of the table, give corresponding z* value. Z* =1. 96 since p(z < 1. 96) = 0. 975. Find z* such that p(z > z*) = . 005.
