MATH302 Week 4 Knowledge Check Homework Practice Questions

1. Question: Find the area under the standard normal distribution to the left of z = -1.05. Round answer to 4 decimal places. 2. Question: Arm span is the physical measurement of the length of an individual's arms from fingertip to fingertip. A man's arm span is approximately normally distributed with mean of 70 inches with a standard deviation of 4.5 inches. Find length in inches of the 99th percentile for a man's arm span. Round answer to 2 decimal places. 3. Question: Find P(-1.96 ≤ Z ≤ 1.96). Round answer to 2 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 $4.59 and a standard deviation of $0.10. Thirty gas stations from the Bay area are randomly chosen. We are interested in the average cost of gasoline for the 30 gas stations. Find the exact probability that the average price for 30 gas stations is less than $4.55. 6. Question: Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years. Find the probability that a light bulb lasts between six and ten years. 7. Question: The average lifetime of a set of tires is three years. The manufacturer will replace any set of tires failing within two years of the date of purchase. The lifetime of these tires is known to follow an exponential distribution. What is the probability that the tires will fail within two years of the date of purchase? 8. Question: The commute time for people in a city has an exponential distribution with an average of 0.5 hours. What is the probability that a randomly selected person in this city will have a commute time between 0.4 and 1 hours? Answer: (round to 3 decimal places) 9. Question: Suppose that the longevity of a light bulb is exponential with a mean lifetime of eight years. Seventy percent of all light bulbs last at least how long? 10. Question: A local pizza restaurant delivery time has a uniform distribution over 0 to 60 minutes. What is the probability that the pizza delivery time is more than 30 minutes on a given day? 11. Question: Miles per gallon of a vehicle is a random variable with a uniform distribution from 25 to 35. The probability that a random vehicle gets between 28 and 33 miles per gallon is: 12. Question: A local grocery delivery time has a uniform distribution over 0 to 60 minutes. What is the probability that the grocery delivery time is more than 15 minutes on a given day? 13. Question: Miles per gallon of a vehicle is a random variable with a uniform distribution from 25 to 35. The probability that a random vehicle gets between 25 and 34 miles per gallon is: 14. Question: The waiting time for a bus has a uniform distribution between 0 and 8 minutes. What is the 90th percentile of this distribution? (Recall: The 90th percentile divides the distribution into 2 parts so that 90% of area is to the left of 90th percentile) _______ minutes 15. Question: The waiting time for a taxi has a uniform distribution between 0 and 10 minutes. What is the probability that the waiting time for this taxi is less than 7 minutes on a given day? 16. Question: The time a student sleeps per night has a distribution with mean 5.9 hours and a standard deviation of 0.4 hours. Find the probability that average sleeping time for a randomly selected sample of 48 students is more than 6 hours per night. 17. Question: A certain brand of electric bulbs has an average life of 300 hours with a standard deviation of 45. A random sample of 100 bulbs is tested. What is the probability that the sample mean will be less than 295? 18. Question: The average amount of a beverage in randomly selected 16-ounce beverage can is 16.1 ounces with a standard deviation of 0.4 ounces. If a random sample of eighty- one 16-ounce beverage cans are selected, what is the probability that mean of this sample is less than 16.2 ounces of beverage? 19. Question: The average amount of a beverage in randomly selected 16-ounce beverage can is 16.1 ounces with a standard deviation of 0.4 ounces. If a random sample of eighty- one 16-ounce beverage cans are selected, what is the probability that mean of this sample is less than 16.2 ounces of beverage? 20. Question: The final exam grade of a statistics class has a skewed distribution with mean of 76 and standard deviation of 7.6. If a random sample of 32 students selected from this class, then what is the probability that average final exam grade of this sample is between 75 and 80?