MATH 21 Worksheet # 5 - Probability Distributions & Binomial Distributions (Sections 6.1 & 6.2) Name Complete the following problems. This worksheet is due on and will count toward 16 worksheet points. When randomly selecting a jail inmate convicted of DWI (driving while intoxicated), the probability distribution for the number x of prior DWI sentences is described in the accompanying table. X P (x) 0.466 1 2 0.187 3 0.042 1. Find the missing probability of the above distribution. 2. Find the probability that an inmate has at least 2 prior DWI's. 3. Find the probability that an inmate has at least 1 prior DWI. 4. What is the expected number of prior DWI's an inmate will have? (Round to 3 decimals.)5. Find the standard deviation. (Round to 3 decimals.) 6. The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, Southwest Air has the best rate with 75% of its flights arriving on time. A test conducted by randomly selecting 15 Southwest flights and observing whether they arrive on time. Find the probability that at most 10 flights arrive on time. Round answer to 4 decimals. Why is this binomial? Number of Trials: Number of Successes: Probability of Success: 7. In a housing study, it was found that 30% of college students live in campus housing. An insurance company wants to sell those students special policies insuring their personal property. If they test a marketing strategy by randomly selecting 20 students, what is the probability that at least three of them lives in campus housing? Round answer to 4 decimals. Why is this binomial? Number of Trials: Number of Successes: Probability of Success