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MATH 302 Quiz 4 Week 4 Knowledge Check – Question and Answers

Part 1 of 6 – Calculations of Probabilities

1.A dishwasher has a mean life of 11.5 years with an estimated standard deviation of 1.5 years (“Appliance life 0.0/ 1.0 Points 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. Find the area under the standard normal distribution to the left of z = -1.35. Round answer to 4 decimal places.

3. Find P(Z > -.98). Round answer to 4 decimal places.

Part 2 of 6 – Continuous Random Variables and Probability Functions

4. Which type of distribution does the graph illustrate?

Part 3 of 6 – The Central Limit Theorem

5. The manufacturer of a new compact car claims the miles per gallon (mpg) for the gasoline consumption is mound-shaped and symmetric with a mean of 27.4 mpg and a standard deviation of 10.2 mpg. If 29 such cars are tested, what is the probability the average mpg achieved by these 29 cars will be greater than 29? math 302 week 4

Part 4 of 6 – The Exponential Distribution

6. The average lifetime of a set of tires is 3.4 years. The manufacturer will replace any set of tires failing within
7. The life of an electric component has an exponential distribution with a mean of 8.9 years. What is the
8. The caller times at a customer service center has an exponential distribution with an average of 22 seconds.
9. The average lifetime of a certain new cell phone is 4.2 years. The manufacturer will replace any cell phone

Part 5 of 6 – The Uniform Distribution

10. Miles per gallon of a vehicle is a random variable with a uniform distribution from 33 to 47. The probability
11. The waiting time for an Uber has a uniform distribution between 5 and 37 minutes. What is the probability
12. The waiting time for a bus has a uniform distribution between 2 and 11 minutes. What is the probability that
13. The waiting time in line at an ice cream shop has a uniform distribution between 3 and 14 minutes. What is
14. The mail arrival time to a department has a uniform distribution over 5 to 45 minutes. What is the probability
15. A local grocery delivery time has a uniform distribution over 15 to 65 minutes. What is the probability that

Part 6 of 6 – Using the Central Limit Theorem Questions 4.0/ 5.0 Points

16. The average amount of a beverage in randomly selected 16-ounce beverage can is 15.85 ounces with a
17. The average amount of water in randomly selected 16-ounce bottles of water is 15.87 ounces with a math 302 week 4
18. The final exam grade of a statistics class has a skewed distribution with mean of 79.8 and standard deviation 1.0/ 1.0 Points 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? Answer: (round to 4 decimal places) ? math 302 week 4
19. The average amount of a beverage in randomly selected 16-ounce beverage can is 15.96 ounces with a
20. The final exam grade of a statistics class has a skewed distribution with mean of 81.2 and standard deviation