Question

4. The promoter of a concert estimates there is a 35% chance the balcony tickets will sell out, there is a 55% that the main floor tickets will sell out, and there is a 15% chance that both will sell out. a. What is the chance that neither of them sell out? (5) b. What is her estimate that at least one of them will sell out? (5) 5. Replacement times for stereos are normally distributed with a mean of 4.5 years and a standard deviation of 1.3 years. b. What percent of all of these stereos last no less than 5.0 years? (10) c. The manufacturer wants to have a warranty so that only 10% of the stereos will have to be replaced free. How long should the warranty be on these stereos ? (10)

Answer 1

Solution ! 1). Griven information, P (balcony tickets will sell out) = 0.35 P (Main floor tickets will sell out) = 0.55 P (Both will sell out) = 0.15 al: P ( neither of them sell out ) = I PLAt least one of them sell out) -1- 0.35 -0.55 +.0115 = 0.25. b). a P ( At least one of them seul out) PLAUB) where, A denote the events that boleony tickets sell out and B denote the events that Main floor tickets will sell out. .. PIHA UB) = PLA) + PID - PLANS) 0.35t orss-ols 0.75.

S Given that, the replacement times for Stedeos are normally distributed Leith of 4.50%. and Standard deviation of 1-3 years, mean Let x denote the replacement times, then, x = N(4.5, 1302) b). The percentage of all of these stessos lost no less than 5 years as given of P(x 25) - P(X- u.S > S-4.5 1-3 1-3 z P/2 > 0.3846). 0.3502 Hence, 35% of all these Sterlos lost gro least than 5.0 years, r. c) Let the warranty be it years longe P(X<t) = 0ilo 2) 8 (t-us a trus) colo

E Plz< trus ) = oilo 1-3 -) t-4.5 Zoigo - 1.3 Swhere, zogo denote upper goy. of Standass zormal variate. =) trueS 103 11 - 1-2815 =) t = 4.51-28150 13 t- 2.83 So, the Washanty should be 3 years, so that only 104. of the Stersos beill be replaced free,