MAT 1120 Name: _________________________ 1. Are the following probability distributions valid probability distributions? Explain why or why not. x P(x) 0 0.15 1 0.35 2 0.25 3 0.20 4 0.05 x P(x) 0 0.3 1 0.3 2 0.2 3 0.2 4 0.15 2. Sam is a representative who sells large appliances such as refrigerators, stoves, and so forth. Let x = number of appliances Sam sells on a given day. Let f = frequency with which Sam had the following sales record. x 0 1 2 3 4 5 6 7 f 12 69 63 41 31 11 10 2 Assume that the sales record is representative of the population of all sales days. a. Use the relative frequency (f / n) to find P(x) for x = 0 to 7. x P(x) 0 1 2 3 4 5 6 7 b. Make a histogram to graph the probability distribution shown in part (a) 1 c. Use the table above to compute the probability that x is between 2 and 5 (including 2 and 5). d. Use the table above to compute the probability that x is less than 3. **Use this table for questions e and f** x P(x) xP(x) x- (x - ) (x - )P(x) e. Compute the expected value of the probability distribution. f. Compute the standard deviation of the probability distribution. 3. Consider a binomial experiment with n = 10 trials where the probability of success on a single trial is p = 0.45. a. Find P(7) b. Find P(x 6) 2 4. The director of a health club conducted a survey and found that 35% of members used only the pool for workouts. Based on this information, what is the probability that, for a random sample of 10 members, 5 used only the pool for workouts? 5. Of those mountain climbers who attempt Mt. McKinley, only 60% reach the summit. In a random sample of 15 mountain climbers who are going to attempt Mt. McKinley, what is the probability of each of the following? a. All 15 reach the summit. b. At least 8 reach the summit. c. No more than 12 reach the summit. d. From 9 to 12 reach the summit, including 9 and 12. 6. A coach found that about 10% of all hockey games end in overtime. What it the expected number of games ending in overtime if 65 hockey games are played as a random sample? 7. There is about 70% probability that a truck will be going over the speed limit on 3 I-80 between Cheyanne and Rock Springs, Wyoming. Suppose that a random sample of five trucks in this stretch is observed. a. Make a histogram showing the probability that r = 0, 1, 2, 3, 4, 5 trucks are speeding. b. Find the mean of this probability distribution. c. Find the standard deviation of this probability distribution. BONUS: Deal or No Deal. You are a contestant with 5 suitcases left: $1 $30,000 $100,000 $300,000 $750,000 The bank offers you $250,000 to walk away from the game. Based on EXPECTED VALUE, do you choose the deal or not? 4