MATH 221 Week 4 Homework

1. Question: The length of time a person takes to decide which shoes to purchase is normally distributed with a mean of 8.54 minutes and a standard deviation of 1.91. Find the probability that a randomly selected individual will take less than 5 minutes to select a shoe purchase. Is this outcome unusual? 2. Question: In a health club, research shows that on average, patrons spend an average of 42.5 minutes on the treadmill, with a standard deviation of 4.8 minutes. It is assumed that this is a normally distributed variable. Find the probability that randomly selected individual would spent between 30 and 40 minutes on the treadmill. 3. Question: A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.98mm and a standard deviation of 0.35mm. Find the probability that a randomly selected tire will have a depth less than 0.50mm. Would this outcome warrant a refund (meaning that it would be unusual)? 4. Question: In an agricultural study, the average amount of corn yield is normally distributed with a mean of 185.2 bushels of corn per acre, with a standard deviation of 23.5 bushels of corn. If a study included 1200 acres, about how many would be expected to yield more than 206 bushels of corn per acre? 5. Question: On average, the parts from a supplier have a mean of 35.8 inches and a standard deviation of 2.4 inches. Find the probability that a randomly selected part from this supplier will have a value between 28.6 and 43.0 inches. Is this consistent with the Empirical Rule of 68%-95%-99.7%? 6. Question: A process is normally distributed with a mean of 10.2 hits per minute and a standard deviation of 1.04 hits. If a randomly selected minute has 12.9 hits, would the process be considered in control or out of control? 7. Question: The candy produced by a company has a sugar level that is normally distributed with a mean of 16.8 grams and a standard deviation of 0.9 grams. The company takes readings of every 10th bar off the production line. The reading points are 17.3, 14.9, 18.3, 16.5, 16.1, 17.4, 19.4. Is the process in control or out of control and why? 8. Question: The toasters produced by a company have a normally distributed life span with a mean of 5.8 years and a standard deviation of 0.9 years, what warranty should be provided so that the company is replacing at most 10% of their toasters sold? 9. Question: A running shoe company wants to sponsor the fastest 5% of runners. You know that in this race, the running times are normally distributed with a mean of 7.2 minutes and a standard deviation of 0.56 minutes. How fast would you need to run to be sponsored by the company? 10. Question: A stock’s price fluctuations are approximately normally distributed with a mean of $26.94 and a standard deviation of $3.54. You decide to sell whenever the price reaches its highest 10% of values. What is the highest value you would still hold the stock? 11. Question: In a survey of first graders, their mean height was 49.5 inches with a standard deviation of 3.6 inches. Assuming the heights are normally distributed, what height represents the first quartile of these students? 12. Question: Hospital waiting room times are normally distributed with a mean of 38.12 minutes and a standard deviation of 8.63 minutes. What is the shortest wait time that would still be in the worst 10% of wait times? 13. Question: The length of timber cuts are normally distributed with a mean of 95 inches and a standard deviation of 0.52 inches. In a random sample of 30 boards, what is the probability that the mean of the sample will be between 94.8 inches and 95.8 inches? 14. Question: Of all the companies on the New York Stock Exchange, profits are normally distributed with a mean of $6.54 million and a standard deviation of $10.45 million. In a random sample of 73 companies from the NYSE, what is the probability that the mean profit for the sample was between -2.9 million and 4.5 million? 15. Question: Doing research for insurance rates, it is found that those aged 30 to 49 drive an average of 38.7 miles per day with a standard deviation of 6.7 miles. These distances are normally distributed. If a group of 60 drivers in that age group are randomly selected, what is the probability that the mean distance traveled each day is between 29.9 miles and 39.9 miles?