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MATH 302 Quiz 4 Week 4 Knowledge Check – Practice Test

Part 1 of 6 – Calculations of Probabilities

1. Find P(Z > -1.24). Round answer to 4 decimal places. Answer: ?
2. Find the area under the standard normal distribution to the left of z = -1.05. Round answer to 4 decimal places.
3. Find P(1.31 < Z < 2.15). Round answer to 4 decimal places. Answer: ?

Part 2 of 6 – Continuous Random Variables and Probability Functions

4. Find the probability that falls in the shaded area.

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 24.6 mpg and a standard deviation of 9.5 mpg. 

If 30 such cars are tested, what is the probability the average mpg achieved by these 30 cars will be greater than 28?
6. The average lifetime of a certain new cell phone is three years. The manufacturer will replace any cell
7. 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?
8. The commute time for people in a city has an exponential distribution with an average of 0.5 hours. math 302 week 4 quiz
9. 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.

Part 5 of 6 – The Uniform Distribution

10. The waiting time for a bus has a uniform distribution between 0 and 10 minutes. What is the
11. The waiting time for a train has a uniform distribution between 0 and 10 minutes. What is the
12. Miles per gallon of a vehicle is a random variable with a uniform distribution from 25 to 35. The
13. The mail arrival time to a department has a uniform distribution over 0 to 60 minutes. What is the
14. Miles per gallon of a vehicle is a random variable with a uniform distribution from 25 to 35. The
15. Miles per gallon of a vehicle is a random variable with a uniform distribution from 25 to 35. The

Part 6 of 6 – Using the Central Limit Theorem

16. The average amount of a beverage in randomly selected 16-ounce beverage can is 16.1 ounces with
17. The final exam grade of a statistics class has a skewed distribution with mean of 76 and standard
18. The time a student sleeps per night has a distribution with mean 5.9 hours and a standard deviation
19. The final exam grade of a mathematics class has a skewed distribution with mean of 78 and standard
20. The final exam grade of a statistics class has a skewed distribution with mean of 78 and standard deviation of 7.8. If a random sample of 36 students selected from this class, then what is the probability that the average final exam grade of this sample is between 75 and 80?