MATH 221 STATISTICS FOR DECISION MAKING WEEK 4 HOMEWORK / 2020
DeVry MATH 221 Week 4 Homework Answers (2020)
1. 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. Monthly water bills for a city have a mean of $108.43 and a standard deviation of $32.09. Find the probability that a randomly selected bill will have an amount greater than $165, which the city believes might indicate that someone is wasting water. Would a bill that size be considered unusual?
3. 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 35 and 48 minutes on the treadmill.
4. A tire company measures the tread on newly-produced tires and finds that they are normally distributed with a mean depth of 0.84mm and a standard deviation of 0.35mm. Find the probability that a randomly selected tire will have a depth less than 0.24mm. Would this outcome warrant a refund (meaning that it would be unusual)?
5. A grocery stores studies how long it takes customers to get through the speed check lane. They assume that if it takes more than 10 minutes, the customer will be upset. Find the probability that a randomly selected customer takes more than 10 minutes if the average is 8.56 minutes with a standard deviation of 1.04 minutes.
6. 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 1100 acres, about how many would be expected to yield more than 190 bushels of corn per acre?
7. On average, the parts from a supplier have a mean of 31.8 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 27.0 and 36.6 inches. Is this consistent with the Empirical Rule of 68%-95%-99.7%?
8. 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 13.9 hits, would the process be considered in control or out of control?
9. The candy produced by a company has a sugar level that is normally distributed with a mean of 16.1 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?
10. 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 5% of their toasters sold?
11. A running shoe company wants to sponsor the fastest 3% of runners. You know that in this race, the running times are normally distributed with a mean of 6.8 minutes and a standard deviation of 0.37 minutes. How fast would you need to run to be sponsored by the company?
12. The weights of bags of peas are normally distributed with a mean of 13.50 ounces and a standard deviation of 1.06 ounces. Bags in the upper 5% are too heavy and must be repackaged. What is the most that a bag can weigh and not need to be repackaged?
13. A stock’s price fluctuations are approximately normally distributed with a mean of $29.51 and a standard deviation of $3.87. You decide to sell whenever the price reaches its highest 20% of values. What is the highest value you would still hold the stock?
14. In a survey of first graders, their mean height was 50.4 inches with a standard deviation of 3.55 inches. Assuming the heights are normally distributed, what height represents the first quartile of these students?
15. 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?
16. A machine set to fill soup cans with a mean of 20 ounces and a standard deviation of 0.11 ounces. A random sample of 22 cans has a mean of 20.04 ounces. Should the machine be reset?
17. 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 45 boards, what is the probability that the mean of the sample will be between 94.5 inches and 95.1 inches?
18. The Dow Jones Industrial Average has had a mean gain of 432 pear year with a standard deviation of 722. A random sample of 40 years is selected. What is the probability that the mean gain for the sample was between 250 and 550?
19. 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 3.0 million and 6.0 million?
20. 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 32.5 miles and 40.5 miles?
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