Exercise 9 The Miramar Company is going to introduce one of the three new products: a widget, a hummer or a nimnot. The market conditions (favorable, stable or unfavorable) will determine the profit or loss the company realizes. The estimated payoffs if widget is introduced are $120,000,$70,000 and $-30,000 respectively for favorable, stable and unfavorable market. The figures for hummer are $60,000,$40,000 and $20,000; and for that of nimnot are $35,000,$30,000 and $30,000 respectively for favorable, stable and unfavorable market conditions. The probabilities for favorable, stable and unfavorable market conditions are 0.2,0.7 and 0.1 respectively. Required: Use decision tree and locate the optimal strategy for the company. Exercise!0 The arrivals at a telephone booth are considered to be following Poisson law of distribution with an average time of 10 minutes between one arrival and the next. Length of the phone call is assumed to be distributed exponentially with a mean of 3 minutes. a. What is the probability that a person arriving at the booth will have to wait? b. What is the average length of queue that forms from time to time? c. The telephone department will install a second booth when convinced that an arrival would expect to wait at least three minutes for the phone. By how much must the flow of arrivals be increased in order to justify a second booth? Exercise 11: On the average, 6.2 cars will arrive at SMU in an hour. a) Compute the probability that exactly 5 cars will arrive in the next hour. b) Compute the probability that no more than 5 cars will arrive in the next hour? Exercise 12: The average salary for DRMC lecturers is $30,000 per year. If the distribution is approximately normal with a standard deviation of $5000, what is the probability that the annual salary of a randomly selected lecturer from the college is a) between $27,500 and $32,500 per year b) less than $25,000 per year.