TUTORIAL CHAPTER 6: CONTINUOUS PROBABILITY DISTRIBUTION 1. For the standard normal probability distribution, the area to the left of the mean is: A. greater than 0.5 B. -0.5 C. one D. 0.5 E. none of the above 2. If a z value is to the left of the mean, then its value is: A. negative B. positive C. any value between -to D. zero E. none of the above 3. Assume z is a standard normal random variable. P(-1.50 < z < 1.90) equals: A. 0.0381 B. 0.9045 C. -0.0381 D. 0.4 E. none of the above 4. Assume z is a standard normal random variable. P(-2.0 < z < -1.0) equals A. 0.8185 B. 0.1469 C. 1.0000 D. 0.1359 E. none of the above 5. Assume z is a standard normal random variable. P(1.20 < z < 1.85) equals A. 0.4678 B. 0.3849 C. 0.8527 D. 0.0829 6. The travel time for a businesswoman traveling between Dallas and Fort Worth is uniformly distributed between 40 and 90 minutes. The probability that she will finish her trip in 80 minutes or less is: A. 0.02 B. 0.2 C. 0.8 D. 1.0 E. none of the above 7. The life expectancy of a particular brand of tire is normally distributed with a mean of 40,000 miles and a standard deviation of 5,000 miles. What is the probability that a randomly selected tire will have a life of at least 30,000 miles? A. 0.4772 B. 0.9772 C. 0.0228 D. none of the above 8. An exponential probability distribution: A. is a continuous distribution B. is a discrete distribution C. can be either continuous or discrete D. none of the above 9. An instructor curves the class grades so that the top 10% of the students in class receive an A for the semester. During the past semester, the grades were approximately normally distributed with a mean of 217 points and a standard deviation of 32 points. How many points were needed to earn an A for the semester? A. 217 B. 230 C. 251 D. 258 10. The graph of which of the following distributions is bell-shaped? A. Exponential B. Normal C. Uniform D. All of the above 11. A bicyclist's one-way commute time is uniformly distributed between 40 and 50 minutes. What is the probability that the commute takes between 44 and 46 minutes? A. 0.2000 B. 0.2736 C. 0.7264 D. 45 minutes E. None of the above 12. A bicyclist's one-way commute time is uniformly distributed between 40 and 50 minutes. What is the expected commute time? A. 5 minutes B. 8.33 minutes C. 45 minutes D. 50 minutes E. None of the above 13. The wind speed at a wind energy farm is approximately normally distributed with a mean of 25 miles per hour and a standard deviation of 7 miles per hour. What percent of the time will the wind speed be below 15 miles per hour? A. 7.64% B. 42.36% C. 57.64% D. 92.36% E. None of the above 14. The wind speed at a wind energy farm is approximately normally distributed with a mean of 25 miles per hour and a variance of 49 miles per hour. When wind speeds exceed 45 miles per hour, the wind farm produces too much electricity for the current transmission lines and must be shut down. What percentage of the time will winds exceed 45 miles per hour? A. 0.21% B. 2.1% C. 9.79% D. 65.91% E. None of the above 15. The time between arrivals of UMS busses at FPEP follows an exponential probability distribution with a mean time between arrivals of 20 minutes. Ali would like to know the probability that the time between two successive arrivals will be 15 minutes or less. A. -0.4724 B. 0.2636 C. 0.5276 D. 0.7364

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