MENDSTATC4 4.E.103. MY NOTES ASK YOUR TEACHER A slot machine has three slots; each will show a cherry, a lemon, a star, or a bar when spun. The player wins if all three slots show the same three items. If each of the four items is equally likely to appear on a given spin, what is your probability ofwinning" (Enter your probability as a fraction.) E MENDSTATC4 4.E.110' MY NOTES ASK YOUR TEACHER A county containing a large number of rural homes is thought to have 60% of those homes insured against fire. Four rural homeowners are chosen at random from the entire population, and X are found to be insured against fire. Find the probability distribution for x. X|U l 2 3 4 mil M ii ll ii What is the probability that at least three of the four will be insured? E The number of companies offering flexible work schedules has increased as companies try to help employees cope with the demands of home and work. One flextime schedule is to work four 10-hour shifts. A survey provided the following information for 214 firms located in two cities in Quebec. Flextime Schedule City Available NotAvailable Total A 37 74 111 B 21 82 103 Totals 58 156 214 A company is selected at random from this pool of 214 companies. (Enter exact numbers as integers, fractions, or decimals.) (a) What is the probability that the company is located in city A7 E (b) What is the probability that the company is located in city 5 and offers flextime work schedules? E (c) What is the probability that the company does not have flextime schedules? E (d) What is the probability that the company is located in city 5, given that the company has flextime schedules available? E A balanced coin is tossed three times. Let X equal the number of heads observed. P(0) = (a) Use the formula for the binomial probability distribution to calculate the probabilities associated with x = 0, 1, 2, and 3. (Enter exact numbers as integers, fractions, or decimals.) D(2) = P(3) = (b) Construct the probability distribution. P(X P(X] 0,4 0.2 0.3 0.1 D.2 0.1 D K 2 3 D 2 p(x) p(x) 0.3 0.3 0.2 0.2 0.1 0.1 WebAssign Plot D 2 3 2 (c) Find the mean and standard deviation of X, using the formulas below. (Round your standard deviation to three decimal places.) H = Ap 7 = Vopq 'd) Using the probability distribution in part (b), find the fraction of the population measurements lying within one standard deviation of the mean. (Enter an exact number as an integer, fraction, or decimal.) Repeat for two standard deviations. How do your results agree with Tchebysheff's Theorem and the Empirical Rule? The results are consistent with Tchebysheff's Theorem but are not consistent with the Empirical Rule. O The results are consistent with the Empirical Rule but are not consistent with Tchebyshell's Theorem. The results are not consistent with Tchebysheff's Theorem or the Empirical Rule. The results are consistent with both Tchebysheff's Theorem and the Empirical Rule