MATH 221 Week 3 Homework; Statistics for Decision-Making

1. Question: Let x represent the number of pets in pet stores. This would be considered what type of variable: 2. Question: Let x represent the height of corn in Oklahoma. This would be considered what type of variable: 3. Question: Consider the following table. If you created the probability distribution for these data, what would be the probability of 40-49? 4. Question: Consider the following table. Find the mean of this variable. 5. Question: Consider the following table. Find the variance of this variable. 6. Question: Consider the following table. Find the standard deviation of this variable. 7. Question: The standard deviation of samples from supplier A is 0.0841, while the standard deviation of samples from supplier B is 0.0926. Which supplier would you be likely to choose based on these data and why? 8. Question: Thirty-five percent of teens buy soda (pop) at least once each week. Eleven kids are randomly selected. The random variable represents the number of these kids who purchase soda (pop) at least once each week. For this to be a binomial experiment, what assumption needs to be made? 9. Question: A survey found that 39% of all gamers play video games on their smart phones. Ten frequent gamers are randomly selected. The random variable represents the number of frequent games who play video games on their smart phones. What is the value of n? 10. Question: Forty-four percent of US adults have little confidence in their cars. You randomly select twelve US adults. Find the probability that the number of US adults who have little confidence in their cars is (1) exactly six and then find the probability that it is (2) more than 7 11. Question: Say a business found that 98.3% of soda cans at a production facility in California are filled correctly. The company chooses 100 juice cans off the production line at that same facility. What assumption must be made for this study to follow the probabilities of a binomial experiment? 12. Question: Eleven baseballs are randomly selected from the production line to see if their stitching is straight. Over time, the company has found that 87.6% of all their baseballs have straight stitching. If exactly seven of the eleven have straight stitching, should the company stop the production line? 13. Question: A bottling company puts 16 ounces of water bottle in each bottle. The company has determined that 94% of bottles have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 12 cans has all cans that are properly filled? 14. Question: A supplier must create metal rods that are 16.4 inches long to fit into the next step of production. Can a binomial experiment be used to determine the probability that the rods are too long, too short, or about right? 15. Question: In a box of 12 pens, there is one that does not work. Employees take pens as needed. The pens are not returned, once taken. You are the 5th employee to take a pen. Is this a binomial experiment? 16. Question: Forty-two percent of employees make judgments about their co-workers based on the cleanliness of their desk. You randomly select 7 employees and ask them if they judge co-workers based on this criterion. The random variable is the number of employees who judge their co-workers by cleanliness. Which outcomes of this binomial distribution would be considered unusual? 17. Question: Eighty-one percent of products come off the line within product specifications. Your quality control department selects 15 products randomly from the line each hour. Looking at the binomial distribution, if fewer than how many are within specifications would require that the production line be shut down (unusual) and repaired? 18. Question: The probability of a potential employee passing a drug test is 86%. If you selected 15 potential employees and gave them a drug test, how many would you expect to pass the test? 19. Question: The probability of a potential employee passing a training course is 86%. If you selected 15 potential employees and gave them the training course, what is the probability that more than 11 will pass the test? 20. Question: Off the production line, there is a 3.7% chance that a candle is defective. If the company selected 45 candles off the line, what is the probability that fewer than 3 would be defective?