Intro to Statistics Homework Chapter 5 Review K Due: Chapter 5 Review and Practice Test Name Free Response 1. If X = the number of televisions in a randomly selected U.S. household, the probability distribution of X is given here. Number of TV's 2 3 4 Probability 0.01 0.21 0.33 0.23 |0.13 1209 a) Explain why this is a valid probability distribution. b) Is X a discrete or a continuous random variable? Explain. c) What is the probability that a randomly selected household has at least 2 televisions? 2. Refer to exercise 1. a) Make a histogram to display the probability distribution of X. b) Calculate and interpret the expected value of X. c) Calculate and interpret the standard deviation of X. 3. To test whether someone has extrasensory perception (ESP), choose I of 4 cards at random - a star, wave, cross, or circle. Ask the person to identify the card without seeing it. Do this a total of 20 times and see how many cards the person identifies correctly. Let X' = number of correct identifications, assuming that the person does not have ESP and is just guessing on each card. a) Explain why X is a binomial random variable. b) Find and interpret the mean of X. c) Find and interpret the standard deviation of X