A​ college's data about the incoming freshmen indicates that the mean of their high school GPAs was

3.5​,

with a standard deviation of

.20​;

the distribution was roughly​ mound-shaped and only slightly skewed. The students are randomly assigned to freshman writing seminars in groups of

25.

What might the mean GPA of one of these seminar groups​ be? Describe the appropriate sampling distribution​ model, including​ shape, center, and​ spread, with attention to assumptions and conditions. Make a sketch using the​ 68-95-99.7 Rule.

the scores of students on the SAT college entrance examinations at a certain high school had a normal distribution with mean μ=536.1μ=536.1 and standard deviation σ=27.9σ=27.9.

(a) What is the probability that a single student randomly chosen from all those taking the test scores 540 or higher?
ANSWER:  

For parts (b) through (d), consider a simple random sample (SRS) of 35 students who took the test.

(b) What are the mean and standard deviation of the sample mean score x¯x¯, of 35 students?
The mean of the sampling distribution for x¯x¯ is:  
The standard deviation of the sampling distribution for x¯x¯ is:

(c) What z-score corresponds to the mean score x¯x¯ of 540?
ANSWER:

(d) What is the probability that the mean score x¯x¯ of these students is 540 or higher?
ANSWER:  

A qualifying exam for a graduate school program has a math section and a verbal section. Students receive a score of 1, 2, or 3 on each section. Define X as a student’s score on the math section and Y as a student’s score on the verbal section. Test scores vary according to the following bivariate probability distribution.

μXX =   , and μYY =   

σXX =   , and σYY =   

The covariance of X and Y is ________ . The coefficient of correlation is _________ . The variables X and Y_______ independent.

The expected value of X + Y is_______ , and the variance of X + Y is ________________ .

To be accepted to a particular graduate school program, a student must have a combined score of 4 on the qualifying exam.

What is the probability that a randomly selected exam taker qualifies for the program?

0.46

0.33

0.47

0.45

Chebysheff’s Theorem states that the proportion of observations in any population that lie within k standard deviations of the mean is at least 1 – 1 / k² (for k > 1).

According to Chebysheff’s Theorem, there is at least a 0.75 probability that a randomly selected exam taker has a combined score between_______ and_______ .

Hallstead Jewelers What have we done? Daddy would know what to do, but I don't. I really thought growing this business would be an easy thing for us, but now I am not so sure. All of the work that we did in 2005 was supposed to set us up for new success, profits, and a bright future. But now, we are showing losses on both the historical investment and on our modernization and expansion. Gretchen Reeves was talking in early February 2007 with her sister and partner Michaela Hurd after receiving preliminary income statements for Halstead Jewelers for fiscal year 2006 which had ended January 31, 2007 (See Exhibit 1). In a new building, just renovated in 2005, with 50% more space and selling staff than ever before, the business had experienced a loss almost double the income of the last "normal" year, 2004. To Gretchen, this did not bode well for the future. The sisters' grandfather established Hallstead Jewelers 83 years earlier in the largest city in the tri-state region. For more than 50 years, until his death, he had nurtured and grown the original store from a start up to one of the largest jewelry and gift stores in the United States. Four departments sold almost everything that customers expected in a jewelry and gift store: fine jewelry and gems, watches, tabletop gifts (china and flatware), and artistic gifts. Customers came from throughout the region to buy from extensive collections in each department. Any gift from Hallstead's had an extra cache attached to it. It was presumed to be the best. When Grandfather died, the store was left to his only son, who had literally grown up in the store to become his father's partner in the business. That son was the father of both Gretchen and Michaela. Another child, their brother James, had shunned the business to study medicine and surgery. The girls, however, followed in their father's footsteps and grew up in the store, learning the business. At the death of their father in 2002, the three children inherited the business as equal partners, and by agreement with James, Gretchen and Michaela took over the management of the business and store. At the time of the sisters' assumption of the ownership and management of the store, it was still operating in the original store location on Lake Avenue and Second Avenue. In the late 1930's, Lake Avenue became the most important retail location in the city. The store was improved and provided elegant space for the display and sale of their products. It was a destination-shopping place. The store was remodeled and redecorated again after the founder died, but the location and space remained the same until 2004.

In the meantime, the principal retail shopping areas shifted two blocks west to Washington Street. Stores were larger there and could accommodate department stores and larger specialty retailers. But reputation and selection still brought customers to Lake Avenue for the selections at Hallstead's. Shopping centers were developed in suburban locations, but Hallstead Jewelers stayed put. The sisters’ father saw the changes in the retail landscape, but he took no action because of them. Hallstead's was a one-store seller at its original location, in many ways an anachronism. By the time the sisters assumed management, there were signs that it might be time for changes. Sales had been stagnant since 1999 or so, and profits were slipping. One of the sisters' first ideas was to look for another or several locations. A consultant said that they needed more space and a fresh store look. Expansion was impossible without moving, and although a move might entail some risk, he recommended that they look toward a larger location on Washington Street. They made some changes in product offerings that offered more sales potential at the cost of minor reductions in margins. In 2004 a large toy seller with more space abandoned the corner of Washington Street and Second Avenue. The sisters wasted no time in signing a new five-year lease and starting extensive and expensive renovations. Since the new store was only two blocks from the original location, Gretchen and Michaela were confident that their loyal customers would find and follow them. Renovations and moving took most of 2005, and they started 2006 in the new store. They laughed about 2005 being a "lost" and "loss" year, but they were sure 2006 would bring a new day to Hallstead's. The retail jewelry business was changing. Tiffany & Company, a business with an origin much like Hallstead Jewelers, had grown into an international powerhouse. With their "blue boxes" they had become the largest diamond seller in the United States. At the same time, a start- up internet seller named Blue Nile, founded in the infancy of the World Wide Web a decade earlier was the second largest diamond seller in the United States. The sisters had not had time to think about what those trends meant for Hallstead's. But as fiscal 2006 ended and the preliminary income statement was in, both Gretchen and Michaela knew something more had to be done. They wanted to figure out what had happened between 2004 and 2006, and they wanted to explore ideas about changes in strategy that would return the business to profitability and a brighter future. Their accountant suggested that the move to a new location had changed the economics of their business somewhat, and that further changes in promotion might be in order. Increasing advertising might bring in more customers, or changing pricing formulas to fend off new internet jewelry competitors might be considered. The sisters put together some questions that they asked the accountant to analyze for them using some additional operating statistics that they had at hand (Exhibit 2).

Exhibit 1 Hallstead Jewelers; Income Statements for Years Ended January 31 (thousands of dollars) 2003 2004 2006 Sales $8,583 $8,102 $10,711 Cost of goods sold 4,326 4,132 5,570 Gross margin $4,257 $3,970 $ 5,141 Expenses Selling expense Salaries 2,021 2,081 3,215 Commissions 429 405 536 Advertising 254 250 257 Administrative expenses 418 425 435 Rent 420 420 840 Depreciation 84 84 142 Miscellaneous expenses 53 93 122 Total expenses $3,679 $3,758 $ 5,547 Net income $ 578 $ 212 $ (406)

Exhibit 2 Hallstead Jewelers Operating Statistics 2003 2004 2006 Sales space (square feet) 10,230 10,230 15,280 Sales per square foot $ 839 $ 792 $ 701 Sales tickets 5,341 5,316 6,897 Average sales ticket $ 1,607 $ 1,524 $ 1,553.

1. Prepare the breakeven point for the years 2003, 2004 and 2006. Calculate the Margin of Safety for each of the years?

2. The following proposals are included the discussion questions of the case (refer to questions 2, 3 and 4 for more details):

a. The Consultant: Reduce price to increase traffic. Reduction in price of 10% will bring the number of tickets to 7,500.   

b. Gretchen: Eliminate sales commission.

c. Michaela: Increase Advertising by $200,000.

For each proposal, calculate operating income and breakeven point.

3. Based on your overall analysis, what market strategies should Hallstead Jewelers adopt? What combination, if any, of the proposals should they consider? Reminder, you cannot assume that they can magically go back to how things were on 2004.

4. What other non-financial business aspects should Hallstead Jewelers consider as part of their strategy for 2007?

During the Great Plague of 1665 in London, medical experts claimed that smoking tobacco would prevent a person from catching the disease. Even school children were ordered to smoke during class, and one boy at Eton was whipped for refusing to smoke. What effect did this have on the market for tobacco? Use a supply and demand diagram to explain.

During the Great Plague of 1665 in London, medical experts claimed that smoking tobacco would prevent a person from catching the disease. Even school children were ordered to smoke during class, and one boy at Eton was whipped for refusing to smoke.What effect did this have on the market for tobacco? Use a supply and demand diagram to explain.(15%)

The pandemic we’re currently living through has impacted all aspects of our lives – work, school, health, family interaction, social connections, recreation and others. In which aspect have you felt the impact of Covid 19 the most? In what ways has it impacted that particular aspect of your life? Write an 5 paragraph essay.

a. Explain the five (5) product levels in the Customer Value Hierarchy.          
b. As a Marketing Consultant employed by Wisconsin International University College, and using the Customer Value Hierarchy as your framework, advise the management of the school about five (5) strategies, with justification, they may need to employ at the different product levels in order to achieve their organizational objective.

Determine the level of measurement for each of the variables: Nominal, Ordinal, Interval - Ratio

               a) Number of people in family

               b) Percentage of university students who attend public school

               c) The rating of the overall quality of a textbook from excellent to poor

               d) Your annual income

               e) The presidential candidate you voted for

               f) Your age