Answer 1-3, 8-15

ilon Denson Random Variables and Probability Distributions Worksheet Inimonid noodleold The mean and the standard deviation of a discrete probability distribution are found by using these formulas: Mean: ul = EXP(x) Standard deviation: o = VE(x - H)2 . P(x) = VE(x2 . P(x)) - 12 1. Discrete or Continuous Random Variables? a. The time it takes a student selected at random to register for the fall semester b . The number or bad checks drawn on Upright Bank on a day selected at random C . The amount of gasoline needed to drive your car 200 miles d. The number of traffic fatalities per year in the state of Florida e . The distance a golf ball travels after being hit with a driver f . The number of ships in Pearl Harbor on any given day 9. Your weight before breakfast each morning 2. Consider each distribution. Determine if it is a valid probability distribution or not, and explain your answer. a. ( clio) adds upto 1 b . not volod adds to 1105 x 0 1 2 x 0 1 2 P(x) 0.25 0.60 0.15 P(x) 0.25 0.60 0.20 3. USA Today reported that approximately 25% of all state prison inmates released on parole become repeat offenders while on parole. Suppose the parole board is examining five prisoners up for parole. Let x = number of prisoners out of five parole who become repeat offenders, and their corresponding probabilities. X 0 1 2 3 4 15 mom toingmoo s lo villidedom offTo P(x) 0.237 0.369 0.264 0.088 0.015 0.001 Iraqifo 001 to inomqide & a a. What is the probability that one or more of the five parolees will be repeat offenders? How does this number relate to the probability that none of the parolees will be repeat offenders? : 163 1-23)=. 763 b. Find the probability that two or more of the five parolees will be repeat offenders. 353 c. Find the probability that two or less of the five parolees will be repeat offenders. d. Compute the mean number of repeat offenders out of five. e. Compute the standard deviation of the number of repeat offenders out of five.8. A hockey goaltender has a save percentage of 0.920. This means that the probability of any single shot taken on the goaltender being a goal is 0.08. What would be the expected number of goals scored on this goaltender in a game where she faced 35 shots? " goals 9. A manufacturer of halogen bulbs knows that 3% of the production of their 100 W bulbs will be defective. What is the probability that exactly 5 bulbs in a carton of 144 bulbs will be defective? 10. A fair die has four faces numbered one to four. What is the probability of rolling a two exactly three times in ten rolls of the die? 11. A packet of carrot seeds has a germination rate of 92%. In other words, the probability of any seed sprouting is 0.92. How many seedlings would you expect in a row of 50 seeds? 12. A packet of vegetable seeds has a germination rate of 96%. What is the probability that exactly 10 of 12 seeds planted will sprout? Problem 13. A student writes a five question multiple-choice quiz. Each question has four possible responses. The student guesses at random for each question. Calculate the probability for each possible score on the test from 0 to 5. 14. There are 10 members on a committee. The probability of any member attending a randomly chosen meeting is 0.9. The committee cannot do business if more than 3 members are absent. What is the probability that 7 or more members will be present on a given date? 15. A salesman has a 20% probability of making a sale to any customer who enters his department. On a typical day, he will meet 30 customers. What minimum number of sales will he have an 88% certainty of making for any given day? or more of the five is to the proballity that us er more of wo or less of