MATH302 Week 4 Test

1. Question: A dishwasher has a mean life of 11.5 years with an estimated standard deviation of 1.5 years ("Appliance life expectancy," 2013). Assume the life of a dishwasher is normally distributed. Find the number of years that the bottom 10% of dishwasher would last. Round answer to 2 decimal places. 2. Question: The size of fish is very important to commercial fishing. A study conducted in 2012 found the length of Atlantic cod caught in nets in Karlskrona to have a mean of 47.8 cm and a standard deviation of 3.72 cm (Ovegard, Berndt & Lunneryd, 2012). Assume the length of fish is normally distributed. What is the length in cm of the longest 10% of Atlantic cod in this area? Round answer to 2 decimal places. 3. Question: Find P(Z -.98). Round answer to 4 decimal places. 4. Question: Find the probability that X falls in the shaded area. 5. Question: The cost of unleaded gasoline in the Bay Area once followed a normal distribution with a mean of $4.74 and a standard deviation of $0.16. Fifteen gas stations from the Bay area are randomly chosen. We are interested in the average cost of gasoline for the 15 gas stations. What is the approximate probability that the average price for 15 gas stations is over $4.99? 6. Question: Suppose that the longevity of a light bulb is exponential with a mean lifetime of 7.6 years. Find the probability that a light bulb lasts between seven and eleven years. 7. Question: The life of an electric component has an exponential distribution with a mean of 7.2 years. What is the probability that a randomly selected one such component has a life less than 4 years? 8. Question: The caller times at a customer service center has an exponential distribution with an average of 22 seconds. Find the probability that a randomly selected call time will be less than 30 seconds? 9. Question: The commute time for people in a city has an exponential distribution with an average of 0.66 hours. What is the probability that a randomly selected person in this city will have a commute time between 0.55 and 1.1 hours? 10. Question: A local grocery delivery time has a uniform distribution over 15 to 65 minutes. What is the probability that the grocery delivery time is more than 20 minutes on a given day? 11. Question: The waiting time for a bus has a uniform distribution between 2 and 13 minutes. What is the probability that the waiting time for this bus is less than 4.5 minutes on a given day? 12. Question: The waiting time for a train has a uniform distribution between 3 and 22 minutes. What is the probability that the waiting time for this train is more than 5 minutes on a given day? 13. Question: The waiting time for a bus has a uniform distribution between 2 and 11 minutes. What is the 75th percentile of this distribution? 14. Question: Miles per gallon of a vehicle is a random variable with a uniform distribution from 22 to 39. The probability that a random vehicle gets between 26 and 31 miles per gallon is: 15. Question: Miles per gallon of a vehicle is a random variable with a uniform distribution from 23 to 47. The probability that a random vehicle gets between 25 and 30 miles per gallon is: 16. Question: The MAX light rail in Portland, OR has a waiting time that is normally distributed with a mean waiting time of 4.22 minutes with a standard deviation of 1.7 minutes. A random sample of 35 wait times was selected, what is the probability the sample mean wait time is under 3.74 minutes? Round answer to 4 decimal places. 17. Question: The average amount of a beverage in randomly selected 16-ounce beverage can is 15.96 ounces with a standard deviation of 0.5 ounces. If a random sample of sixty- five 16-ounce beverage cans are selected, what is the probability that the mean of this sample is less than 16.05 ounces of beverage? 18. Question: The time a student sleeps per night has a distribution with mean 6.06 hours and a standard deviation of 0.55 hours. Find the probability that average sleeping time for a randomly selected sample of 35 students is more than 6.15 hours per night. 19. Question: The final exam grade of a statistics class has a skewed distribution with mean of 79.8 and standard deviation of 8.2. If a random sample of 45 students selected from this class, then what is the probability that the average final exam grade of this sample is between 80 and 83? 20. Question: The average amount of water in randomly selected 16-ounce bottles of water is 16.15 ounces with a standard deviation of 0.45 ounces. If a random sample of thirty-five 16-ounce bottles of water are selected, what is the probability that the mean of this sample is less than 15.99 ounces of water?