Chapter 5 Discrete Probability Distributions ded limonil da a. Compute the probability that exactly 4 of the 20 Americans surveyed are satisfied with the way things are going in the United States. b. Compute the probability that at least 2 of the Americans surveyed are satisfied with the way things are going in the United States. c. For the sample of 20 Americans, compute the expected number of Americans who are satisfied with the way things are going in the United States. d. For the sample of 20 Americans, compute the variance and standard deviation of the number of Americans who are satisfied with the way things are going in the United States. 43. According to a 2010 study conducted by the Toronto-based social media analytics firm Sysomos, 71% of all tweets get no reaction. That is, these are tweets that are not replied to or retweeted (Sysomos website, January 5, 2015). Suppose we randomly select 100 tweets. a. What is the expected number of these tweets with no reaction? b. What are the variance and standard deviation for the number of these tweets with no reaction? 5.6 Poisson Probability Distribution In this section we consider a discrete random variable that is often useful in estimating the number of occurrences over a specified interval of time or space. For example, the random bability variable of interest might be the number of arrivals at a car wash in one hour, the number ten used to of repairs needed in 10 miles of highway, or the number of leaks in 100 miles of pipeline. arrivals in If the following two properties are satisfied, the number of occurrences is a random variable ations. described by the Poisson probability distribution. upaword tomanni OS PROPERTIES OF A POISSON EXPERIMENT 1. The probability of an occurrence is the same for any two intervals of equal length. 2. The occurrence or nonoccurrence in any interval is independent of the occur- rence or nonoccurrence in any other interval. The Poisson probability function is defined by equation (5.15). and seoyou? ( n taught t the Ecole POISSON PROBABILITY FUNCTION in Paris 808. In f( x) - Mer shed a work (5.15)