Gifted/ Accelerated Math 3

Gifted/ Accelerated Math 3 Name: ______Statistics Final Exam Review Date: ______

1. The mean lifetime of all home heaters of a certain brand is 9.5 years. A random sample of 30 home heaters is taken and the average lifetime of these heaters is 8.2 years. What is the population? a. All home heaters that have failed. b. All home heaters with a lifetime of 9.5 years. c. All home heaters that have been sold. d. All home heaters ever produced.

2. The owner of a large fleet of courier vans is trying to estimate her costs for next years operations. A random sample of 8 vans yields the following fuel consumption data: 10.3 9.7 10.8 12.0 13.4 7.5 8.2 9.1 Calculate the mean and standard deviation of the sample.

Find the probabilities of the following z-scores. 3. P(z < 1.68)

4. P(z > 1.13)

5. P( -0.80 < z < -0.15)

6. P( 1.21 < z < 1.87)

7. What is the z-score that corresponds to the 75th percentile?

8. At a company, the mean starting salary is $35,000 and the standard deviation is $2,500. What’s the probability that someone has a starting salary of $32,500 or less?

9. The mean and standard deviation are $288 and $121.33 respectively for amount of money spent on textbooks. What’s the probability that a random student will spend $265 or less for books?

10. The braking distance for a certain vehicle on a dry surface is normally distributed with a mean of 160 feet and standard deviation of 5 feet. Approximately, what percentage of the braking distances is between 150 and 170 feet?

11. The distribution of the heights of students in a large class is roughly bell-shaped. Moreover, the average height is 68 inches, and approximately 95% of the heights are between 62 and 74 inches. Find the standard deviation of the height distribution. 12. The Beanstalk Club is limited to women and men who are very tall. The minimum height requirement for women is 70 inches. Women's heights have a mean of 63.6 in. and a standard deviation of 2.5 in. What percentage of women could be in the Beanstalk club, meaning they have a height of 70 inches or higher.

13. On a certain test the mean for the class was 87.5 with a standard deviation of 3.1. If someone made in the top 15% of the class, what grade did the earn on the test?

14. Grades on a Chemistry test follow a normal distribution with a mean of 65 and a standard deviation of 12. Approximately what percentage of the students has a score below 50?

15. Sketch a normal distribution and plot and label the properties of the Empirical Rule.

16. Consider a large population with   9 0 and   18 . Find the mean and standard deviation of the _ _ sample mean, x , for a sample size of: a. 20   b. 45 

17. Common Confidence Intervals: What are the corresponding z-scores to 90%, 95%, and 99% confidence intervals?

18. By 2011 the average household in Georgia owned an average of 4.1 television sets with a standard deviation of 2.3. A simple random sample was taken of 50 households in Augusta and found that they owned an average of 3.4 television sets. What is the probability that any random sample of 50 households would own an average of 3.4 television sets of more?

19. By 2011 approximately 80% of the population owned a television set. In a group of 100 people chosen at random, what is the probability that 75 of them or more own a television set?

20.The National Center for Education Statistics surveyed 4400 college graduates about the lengths of time required to earn their bachelor's degrees. The mean of the sample is 5.15 years. It is known that the population standard deviation is 1.68 years. Construct the 95% confidence interval for the mean time required by all college graduates.

21. In crash test of 15 Honda Odyssey minivans, collision repair cost are found to have a distribution that is roughly bell shaped, with a mean of $1786 and a population standard deviation of $937 (based on data from the Highway Loss Data Institute). Construct the 99% confidence interval for the mean repair cost in all such vehicle collisions. Answers: 1. D 2. X-bar = 10.125; standard deviation of the sample = 1.95 3. 0.9535 4. 0.1292 5. 0.2282 6. 0.0824 7. 0.67 or 0.68 8. 0.1587 9. 0.4247 10. 95.44% 11. 3 12. 0.0052 13. 91 14. 10.56% 15. 16. A. mean x-bar = 90; s.d. of x-bar = 4.02 B. mean x-bar = 90; s.d. of x-bar 2.68 17. 90%--> 1.645; 95%--> 1.96; 99%--> 2.576 18. 0.5871 19. 0.8944 20.[5.10, 5.2] 21. $1162.78, $2409.22