business statistics sampling and distributions

Hi, please help me with these 3 questions. Can you complete by Wednesday night (3/20) ? Let me know if there are any questions. You will need to submit your supporting formula work or work in Excel.

USAA, the United Services Automobile Association, is a diversified financial services group of companies based in San Antonio, Texas. Currently, ranked 57th in net worth ($25 billion) and 141st in revenue in Fortune 500 companies, USAA offers banking, investing, and insurance to people and families that serve, or served, in the United States military. At the end of last year, there were 10.7 million members, 42.6 million products, and 26,300 employees. It is the 5th largest homeowners’ insurer and the 6th largest auto insurer.

USAA was founded in 1922 by 25 army officers who came together in San Antonio and decided to insure each other’s automobiles. In the 1930s, even with the great depression, the number of employees doubled from 46 to 99. By 1940, there were 30,000 members including 60% of all eligible U.S. military officers. During the 1940s, in spite of a decrease in driving due to wartime restrictions on gasoline, spare parts, and tires, USAA grew rapidly and reported a profit of over $3 million. At the end of the 1950s, profits were over $14 million. In 1961, USAA’s bylaws were changed such that membership no longer had to be relinquished when an officer leaves the service. In 1963, the USAA Life Insurance Company was formed; and by the end of 1969, there were 700,000 members producing a profit of almost $24 million.

In 1977, USAA reached $1 billion in assets; and in 1983 they opened the USAA Federal Savings Bank. Fortune magazine named USAA one of “America’s Most Admired Companies” in 1992 and Money magazine named USAA Federal Savings Bank the best bank in America. By the turn of the century, USAA owned and operated a total of $58.9 billion assets. By 2003, 96% of all active-duty officers and 44% of enlisted personnel were USAA members. USAA introduced a car-buying service in 2008; and in 2009, the company expanded its eligibility to all who are serving or have honorably served our nation in the U.S. military and their families. In 2011, Fortune magazine included USAA on its list of “100 Best Companies to Work For” for the third straight year.

According to their mission statement, “USAA’s mission is to facilitate the financial security of its members, associates and their families by providing a full range of highly competitive financial products and services. In so doing, we seek to be the provider of choice for the military community.”

Question #1:

2. A study by Quadrant Information Services commissioned by calculated auto insurance rates for each of the 50 states; and as a result, the average annual rate for the United States was $1317. Suppose annual rates of auto insurance in the United States are normally distributed with a standard deviation of $324. Based on these data, what is the probability that a randomly selected auto insurance rate in the United States would be greater than $1750? What percentage of auto insurance rates would be less than $1200? What percentage of auto insurance rates would be between $1100 and $1500?


The 3M company is a global innovation company with over 100,000 patents, $31 billion in sales, and 90,000 employees. 3M has 27 business units organized under five business groups: consumer, electronics & energy, health care, industrial, and safety & graphics. It has 46 technology platforms including adhesives, abrasives, electronics & software, light management, microreplication, nanotechnology, nonwoven materials, and surface modification. Related to this,3M has 8,500 researchers worldwide and its products are sold in nearly 200 countries. Included in 3M’s more widely-known products are Scotch®Tape, Post-it®Notes, and Aceâ„¢ bandages.

3M was born as a small-scale mining company in 1902 when the five founders invested in harvesting a mineral known as corundum from a mine in Minnesota on the shores of Lake Superior. The mine ultimately did not produce much corundum, but the company used a spirit of innovation, collaboration, and technology to discover other materials and products that could be of use to consumers and companies. In 1910, the company, then known as Minnesota Mining and Manufacturing (3M), moved its headquarters to St. Paul where it is today. In the early 1920s, 3Mcreated the world’s first waterproof sandpaper which helped open up opportunities for the company in the automotive industry. In 1925, a young lab assistant invented masking tape thereby helping to diversify the company’s offering. Over the next few decades, many of the “scotch” products were developed and marketed including scotch tape, scotlite and Scotchgard. In the 1960’s, 3M introduced dry silver microfilm, photographic products, carbonless papers, overhead projection systems and numerous health care and dental products. In 1980, 3M introduced post its which created a new category in the marketplace. By the year 2000, there were new products such as post it super sticky pads, scotch transparent duct tape, optical films for LCD tvs and a family of new scotch brite cleaning products. In 209, they introduced a new line of stethoscopes and health care and introduced new products in the is grinding industry. In later years, 3M developed 3M solar mirror film 1100 for concentrated solar power.

Today, 1/3 of 3M sales come from products invented within the past 5 yrs, during which time over 8 billion has been invested in R&D and related expenditures. According to company information, the global 3M team is committed to creating the technology and products that advance every company, enhance every home and improve every life. 3M has been listed on the dow jones sustainability index for 15 consecutive years.

Question #2

3M has developed a composite measure, a3M Value Index Score, which provides a standard metric to assess accountable value in health care. This index care domains derived from 16 measures of key processes and outcomes that effectvalue in health care. According to 3M, this Value Index Score can increase the understanding f provider and system performance thereby accelerating and prioritizing the areas where improvement is needed. This measure can be used by both providers and payers to help improve patient outcomes and to control costs.Suppose you were asked to develop a sampling plan for a study to determine the value index, and general attitudes toward the index, what sampling plan would you use?What is the target population(or are there multiple target populations)?Which of the four types of random sampling discussed in the chapter would you use and why? If you were to use stratified random sampling, what would be your strata?


Question #3:

In a particular area of the Northeast, an estimated 75% of the homes use heating oil as the principal heating fuel during the winter. A random telephone survey of 150 homes is taken in an attempt to determine whether this figure is correct. Suppose 120 of the 150 homes surveyed use heating oil as the principal heating fuel. What is the probability of getting a sample proportion this large or larger if the population estimate is true?

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