Statistics Review Chapter 6

1. StatisticsReview Chapter 6 • Normal Distributions • Control Charts • Z-score vs raw score • Table is area under curve to the left • Given area,find z-score • For binomial to approximate normal, np>5 and nq>5 • Continuity correction

2. 1 • The running times of feature movies have a mound shaped distribution with mean =110 minutes and standard deviation of 30 minutes. • Use the empirical rule to find an interval centered about the mean in which about 68% of the data will fall • Estimate a range of values centered about the mean in which about 95% of the data will fall

3. 2 • The percentage growth rate of stocks of companies that specialize in recreation equipment and appliances has a mound shaped distribution with mean estimated to be 13.1% and standard deviation 6.0%. • Estimate a range of values centered about the mean in which 68% of the data will fall • Estimate a range of values centered about the mean in which 95% of the data will fall

4. 3 • The highway patrol has a target of 28 traffic tickets per week with standard deviation 5 tickets per week for a stretch of mountain highway. The number of tickets issued for 15 consecutive weeks is given below. T= number of week, x = number of tickets • T 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 • x 22 20 15 16 25 30 30 34 30 32 36 40 33 35 30 • Make a control chart for the data above • Determine whether the process is in statistical control. If not, specify which out of control signals are present

5. 4 • Last fiscal year, the average number of defective televisions produced by a factory each day was 17.6, with standard deviation of 5.2. For the first 10 days of this fiscal year, the number of defective televisions produced is shown in the following table: • Day 1 2 3 4 5 6 7 8 9 10 • Def tv 19 15 13 16 24 29 34 25 20 10 • Make a control chart for the daily number of defective televisions produced • Do the data indicate that the production is “in control;”? Explain

6. 5 • Troy took a standardized test to try to get credit for first-year Spanish by examination. His standardized score was 1.9. The mean score for the exam was 100 with standard deviation 12. The language department requires a raw score if 120 to get credit by exam for first-year Spanish. • Compute Troy’s raw score • Will Troy get credit for first year Spanish based on this exam?

7. 6 • The snow pack on the summit of Wolf Creek Pass, Colorado on March 1 has been measured for many years. It is normally distributed with mean 78.1 inches and standard deviation of 10.4 inches. A year is selected at random. • Find the probability that the snowpack is less than 60 inches • Find the probability that the snowpack is more than 85 inches • Find the probability that the snowpack is between 60 and 85 inches

8. 7 • The life of Corn Delight popcorn maker is normally distributed with mean 20 months and standard deviation 2 months. The manufacturer will replace a Corn Delight popper is it breaks during the guarantee period. • If the manufacturer guarantees the popper for 18 months what fraction of the poppers will he probably have to replace • How long should the guarantee period be if the manufacturer does not want to replace more than 3% of the poppers

9. 8 • Let x represent the life the a AA battery in a portable radio. The x distribution has mean 44 hours and standard deviation 3.6 hours. Convert each of the following x intervals into z intervals. • 40 < x < 46 • 37 < x < 51 • 41 < x < 45

10. 9 • David and Laura are both applying for a position of the ski patrol. David took the advanced first aid class at his college. His score on the comprehensive final exam was 173 points. The final exam scores followed a normal distribution with mean 150 points and standard deviation 25 points. Laura took an advanced first aid class at the plant where she works, For the method of testing there her cumulative scored on all exams was 88. The cumulative scores followed a normal distribution with mean 65 and standard deviation 10. Both courses are comparable in content and level of difficulty. There is only one position available on the ski patrol and David and Laura are equally qualified skiers. • Both David and Laura scored 23 points above the mean for their respective tests. Does this mean they both gave the same performance on the first aid course? Explain • Calculate the z scores for David and Laura. On the basis of test results which of them should get the job. Explain

11. 10 • A certain portable CD player is known to function properly for a mean 3.6 years with a standard deviation of .6 year. The player is sold with a 3 year warranty. What is the probability that the player will break during the warranty period?

12. 11 • Find z such that 80% of the area under the standard normal curve lies between –z and z

13. 12 • The probability of an adverse reaction to a flu shot is 0.02. It the shot is given to 1000 people selected at random, what is the probability that: • 15 or fewer people will have an adverse reaction • 25 or more people will have an adverse reaction • Between 20 and 30 people will have an adverse reaction

14. 13 • On Professor Grindstone’s final exam, the mean score was 78 and the standard deviation was 10. He wants to “curve” the exam so that the middle 50% of the students get C’s. • Find a z score for which the area under the standard normal curve form –z to z is 50% • Find the range of schores which will be assigned a grade of C

15. 14 • The number of visitors per day at a national park during the summer months follows a normal distribution with mean 10500 and standard deviation 2750. For a summer day chosen at random, • Find the probability that the number of visitors will be between 6000 and 15000 • Find the probability that the number of visitors will be less than 5000