MATH 221 Week 3 Homework; Statistics for Decision-Making

1. Question: Let x represent the number of cars in a parking lot. This would be considered what type of variable: 2. Question: Let x represent the number of players on a sports field. 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 18-29? 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 0.4582, while the standard deviation of samples from supplier B is 0.3358. Which supplier would you be likely to choose based on these data and why? 8. Question: Ten frequent gamers are randomly selected. The random variable represents the number of frequent gamers who play video games on their smart phones. For this to be a binomial experiment, what assumption needs to be made? 9. Question: A survey found that 75% of all golfers play golf on the weekend. Eighteen golfers are randomly selected. The random variable represents the number of golfers that play on the weekends. What is the value of p? 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 45% of customers in Detroit, MI prefer green sweaters. The company chooses 8 customers in Austin, TX and asks them if they prefer green sweaters. What assumption must be made for this study to follow the probabilities of a binomial experiment? 12. Question: Eight baseballs are randomly selected from the production line to see if their stitching is straight. Over time, the company has found that 93.8% of all their baseballs have straight stitching. If exactly six of the eight have straight stitching, should the company stop the production line? 13. Question: A soup company puts 12 ounces of soup in each can. The company has determined that 97% of cans have the correct amount. Which of the following describes a binomial experiment that would determine the probability that a case of 36 cans has all cans that are properly filled? 14. Question: A supplier must create metal rods that are 2.3 inches width to fit into the next step of production. Can a binomial experiment be used to determine the probability that the rods are the correct width or an incorrect width? 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 5 employee to take a pen. Is this a binomial experiment? 16. Question: Eighty-two percent of employees make judgments about their coworkers 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: Seventy-six 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 12 or more 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?