Q4.(15) One random sample of the height of one type of tree was recorded. 7, 9 ,10, 7 ,12 ,10, 8, 13 ,15, 9 1.(5) Apply the backward empirical rule to check normality of the data, and conclude if any evidence of non-normality. 2) Assume the height of the tree is normal, calculate the 99% two-sided confidence interval for the true population average height. 3.(5) Assume that we know the population variance σ2=9, and we request the bound on the error of estimation of 99% confidence interval to be 2, find the minimum sample size n.

Consider a small town, with two restaurants: a tapas bar and a bistro. Both restaurants have a set menu and the cost of serving each customer is $8 for both restaurants. Tapas bar chooses its price for the menu denoted by Pt, and bistro chooses its price for the menu denoted by Pb. Both restaurants are trying to maximize their profits. Tapas bar faces the demand curve Qt = 44 − 2Pt + Pb and bistro faces the demand curve Qb = 44 − 2Pb + Pt.

a) Write down the profit function of the tapas bar.

b) Write down the profit function of the bistro.

c) Find the best reply function of the tapas bar.

d) Find the best reply function of the bistro.

e) Find the Nash equilibrium using the best reply functions you derived in part c and d.

f) Draw the best reply functions you found in part c and d in the same graph. Show the Nash 2 equilibrium on your graph.

g) Does the Nash equilibrium you found generate the highest possible total profits (that is the sum of profits of the tapas bar and the profits of the bistro) for the two firms? If so, argue why this is the case. If not, argue why this is not the case and find the point that generates the highest possible total profits for the two firms.

Mindy Lee was a software engineer who worked for a company that is known for its inventory management software suite. She specialized in designing interfaces that help a business migrate its inventory data to cloud computing. Mindy has loved the Internet since her school years; she used email and browsers before any other kid in her class. She books all her travel arrangements online, including flights, car rentals and hotel rooms. Mindy has inherited money and invested in a small hotel, the Sunrise, a 140-room independent, limited service midscale property. She has 80% ownership and her silent partner owns the other 20%, allowing Mindy total control in operating decisions. The hotel has a lot of potential, as the area in which it is located is popular with tourists. There are two similar hotels nearby. Over the years, however, it has struggled to gain market share. The previous owner, an old hotelier, had refused to consider a franchise agreement, hoping to compete on service quality and reputation. The average annual occupancy at the Sunrise for the last two years (prior to Mindy’s ownership) was 40%. The average rate for the last two years (prior to Mindy’s ownership) was $130. Mindy doesn’t pretend to know how to run a hotel’s daily operations, but is convinced that she can boost sales by embracing OTAs to sell her rooms. She pins her high hopes on working with Expedia. After her first two quarters (6 months) of being in charge, monthly occupancy has averaged 70%-a significant improvement. The hotel’s CPOR (cost per occupied room) is unchanged, at $40. Her ranking on Expedia has the hotel on the first page for guest searches. Overall hotel ADR however, has dropped significantly to $110, even before Expedia’s 25% margin is factored in. As agreed with the Expedia Market Manager, the hotel is selling its rooms at a lower rate on Expedia vs. their own website (Sunrise.com), for additional exposure. Almost all rooms are now being booked on Expedia. Even regular guests no longer use the Sunrise website.

Using case study format (see rubric), address the situation. Your submission should be 2 pages, double spaced, not including references and cover page. Here are some points to consider / incorporate: Rate parity, positioning vs comp set, distribution costs, conversion to Brand.com, service levels, ADR vs. RevPAR, GOPPAR.

As a consultant, brought in to make recommendations, what do you think Mindy should do, and why?

For the data set shown​ below

x   y
20   98
30   95
40   91
50   83
60   70

​(a) Use technology to find the estimates of β0 and β1.

β0≈b0equals=114.60

​(Round to two decimal places as​ needed.)

β1≈b1=−0.68

​(Round to two decimal places as​ needed.)

​(b) Use technology to compute the standard​ error, the point estimate for σ.

Se=__?__

​(Round to four decimal places as​ needed.)

Design and implement a function which has one input parameter which is a number which is greater than 50, called num. Then the function will create a dictionary whose keys are 2 and 3 and 4 and 5 and 6 and 7 and 8 and 9. Then the function calculates the values for each of the above keys. The value for a key is all the numbers between 2 and input “num” that are divisible by the key. The function eventually will print the result. - Hint: Use a dictionary whose values are lists. - Example: num = 20 2: [2,4,6,8,10,12,14,16,18,20] 3: [3,6,9,12,15,18] 4: [4,8,12,16,20] 5: [5,10,15,20] 6: [6,12,18] 7: [7, 14] 8: [8, 16] 9: [9, 18]. write a python program for this question. use main function.

Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a seven-lap race) with a standard deviation of 2.28 seconds. The distribution of her race times is normally distributed. We are interested in one of her randomly selected laps.

A)Find the percent of her laps that are completed in less than 131 seconds. (Round your answer to two decimal places.)

B) The fastest 4% of her laps are under how many seconds? (Round your answer to two decimal places.)

C)

The middle 80% of her lap times are from ___  seconds to ___

• Assume that you recently graduated with a major in finance and just landed a job in the trust department of a large regional bank. Your first assignment is to invest $100,000 from an estate for which the bank is trustee. Because the estate is expected to be distributed to the heirs in approximately one year, you have been instructed to plan for a one-year holding period. Furthermore, your boss has restricted you to the following investment alternatives, shown with their probabilities and associated outcomes. The bank’s economic forecasting staff has developed probability estimates for the state of the economy, and the rate of return on each alternative is estimated under each state of the economy. High Tech, Inc., is an electronics firm; Collections, Inc., a firm collects past-due debts; and U.S. Rubber manufactures tires and various other rubber and plastic products.

• Given the situation as described, discuss the following questions:

  1. Calculate the expected rate of return on each alternative. Which alternative has the highest return and which one has the lowest return?
  2. Calculate the riskiness of each alternative using the standard deviation of returns. What type of risk does the standard deviation measure?
  3. Calculate the coefficient of variations (CVs) for the different securities and rank the alternatives based on the CVs. Does the CV measurement produce the same risk rankings as the standard deviation?
  4. Suppose you created a two-stock portfolio by investing $50,000 in High Tech and $50,000 in Collections. Calculate the expected return rP , the standard deviation ( δp), and the coefficient of variation (CVp) for this portfolio. How does the riskiness of this two-stock portfolio compare to the riskiness of the individual stocks if they were held in isolation?
  5. Suppose an investor starts with a portfolio consisting of one randomly selected stock. What would happen (1) to the riskiness and (2) to the expected return of the portfolio as more randomly selected stocks are added to the portfolio? What is the implication for investors? Draw two graphs to illustrate your answer.

• Refer to the table below:

Compare and contrast prejudice and discrimination, offering one to two similarities (comparisons) and one to two differences (contrasts). Robert Merton's diagram about prejudice and discrimination contains four cells: active bigot, timid bigot, fair-weather liberal, all-weather liberal. For each cell, define and give an example of a person who fits the category. In your view, which type is the most dangerous for society, and why?

Consider the following table:

Step 1 of 8 : Calculate the sum of squares among treatments. Please round your answer to two decimal places.

Step 2 of 8: Calculate the degrees of freedom among treatments.

Step 3 of 8: Calculate the mean square among treatments. Please round your answer to two decimal places.

step 4 of 8 Calculate the F-value. Please round your answer to two decimal places.

step 5 of 8 What is the sum of squares of sample means about the grand mean? Please round your answer to two decimal places.

Step 6 of 8: What is the variation of the individual measurements about their respective means? Please round your answer to two decimal places.

Step 7 of 8: What is the critical value of F ? Please round your answer to four decimal places, if necessary.

Step 8 of 8: Is F significant

Calculate the sum of squares of experimental error. Please round your answer to two decimal places.