# According to the National Association of Childcare Resources and Referral Agencies, the average cost of care for an infant in a child-care center in Delaware was $8,769 a year

According to the National Association of Childcare Resources and Referral Agencies, the average cost of care for an infant in a child-care center in Delaware was $8,769 a year. Assume this cost follows a normal distribution with a standard deviation of $925. a. What is the probability that a randomly selected child-care center in Delaware costs 1. more than $8,000 per year for infant care? 2. more than $9,000 per year for infant care? 3. between $8,500 and $9,500 per year for infant care? b. Use Excel to confirm the answers in part a. c. Determine the rate a child-care center that wishes to be in the 60th percentile in the state of Dela-ware should charge for an infant.

Assume that the number of miles a particular brand of tire lasts before it needs to be replaced follows a normal distribution with a mean of 45,600 miles and a standard deviation of 5,800 miles. a. What is the probability that the next tire of this brand sold will last 1. more than 36,000 miles before it needs to be replaced? 2. less than 42,000 miles before it needs to be replaced? 3. between 45,000 and 55,000 miles before it needs to be replaced? b. Use Excel to confirm the answers in part a. c. What is the mileage that 90% of the tires of this brand will survive before needing to be replaced?

3. On weeknights, the average number of hours of sleep per night for adults 55–84 years old is 7.0. Assume this random variable follows a normal distribution with a standard deviation of 1.1 hours. a. What is the probability that a randomly selected adult from this age group will get 1. more than 6.0 hours of sleep tonight? 2. fewer than 5.0 hours of sleep tonight? 3. between 6.3 and 8.0 hours of sleep tonight? 4. between 5.6 and 6.5 hours of sleep tonight? b. Use Excel to confirm the answers in part a. c. How many hours of sleep will an adult in this age group get if they are in the 35th percentile?

4. TomTom, the producer of GPS devices, reported that the fastest drivers in the nation are in Mississippi. In Mississippi, interstate drivers average 70.1 miles per hour. Assume that the

speed of cars traveling on Mississippi’s interstates follows the normal distribution with a standard deviation of 7.2 miles per hour. a. What is the probability that a randomly selected car on a Mississippi interstate is traveling 1. faster than 65 miles per hour? 2. slower than 72 miles per hour? 3. between 60 and 66 miles per hour? 4. between 78 and 85 miles per hour? b. Confirm the answers to part a with Excel. c. What average speed should I drive if I want to travel faster than 70% of the cars on the interstate?

5. In a recent USA Today article titled Consumers Are Caught in a Sugar Battle, Americans consume an average of 22.2 teaspoons of sugar per day. Assume daily sugar consumption follows the normal distribution with a standard deviation of 6.5 teaspoons. a. What is the probability that a randomly selected American will consume 1. more than 25 teaspoons of sugar today? 2. between 20 and 27 teaspoons of sugar today? 3. between 10 and 18 teaspoons of sugar today? 4. between 28 and 35 teaspoons of sugar today? b. Confirm the answers to part a with Excel. c. How many teaspoons of sugar will a person consume today if he or she is in the 65th percentile?

6. The RAD Construction Company has been awarded a contract with the state of Delaware to replace a bridge on Pike Creek Road. Based on experience with previous projects, RAD feels the project completion time follows a normal distribution with a mean of 92 days and a standard deviation of 9 days. RAD anticipates the net profit for completing the project is $125,000. If the company completes the project in less than 84 days, it will receive an additional $20,000 bonus from the state. If it takes longer than 106 days to complete the project, the state of Dela-ware will penalize RAD $15,000. What is RAD’s expected profit for the project?

7. According to the Bureau of Labor Statistics, the un-employment rate for workers aged 20 to 24 in April 2018 was 6.7%. Consider a random sample of 110 workers from this age group.

a. What is the probability that 10 or fewer will be unemployed? b. What is the probability that 5 or fewer will be unemployed? c. What is the probability that between 5 and 15 of them will be unemployed?

8. According to the Beverage Marketing Corporation, the per capita consumption of bottled water in the United States is 2.3 gallons per month. Assume the standard deviation for this population is 0.75 gallons per month. Consider a random sample of 36 people. a. What is the probability that the sample mean will be less than 2.1 gallons per month? b. What is the probability that the sample mean will be more than 2.2 gallons per month? c. Identify the symmetrical interval that includes 95% of the sample means if the true population mean is 2.3 gallons per month.

9. According to the U.S. Energy Information Adminis-tration, regular gasoline averaged $2.65 per gallon in the United States in April 2018. Assume the standard deviation for gasoline prices is $0.12 per gallon. A random sample of 30 service stations was selected. a. What is the probability that the sample mean will be less than $2.66? b. What is the probability that the sample mean will be more than $2.63? c. What is the probability that the sample mean will be between $2.62 and $2.72? d. Suppose the sample mean is $2.71. Does this result support the findings of the U.S. Energy Informa-tion Administration? Explain your answer.

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