Make a Frequency Distribution Chart for the following set of Data 50, 10, 25, 20, 20, 20, 50,100, 30, 15

Although bats are not known for their eyesight, they are able to locate prey (mainly insects) by emitting high-pitched sounds and listening for echoes. A paper gave the following distances (in centimeters) at which a bat first detected a nearby insect. 23 40 27 56 52 34 42 61 68 45 83 (a) Compute the sample mean distance at which the bat first detects an insect. (Round your answer to three decimal places.) cm (b) Compute the sample variance and standard deviation for this data set. (Round your answers to two decimal places.) Variance?

Standard deviation?

Helena Lorimer runs a set of ice cream cafes that sell mainly three flavors of ice cream: vanilla, chocolate, and strawberry. Hot weather and high demand have caused her to run short of the main ingredients: milk, sugar, and cream. She has decided to make the best assortment of ice cream quantities in these three flavors and ration out the deliveries to the cafes.

She has collected data on the profitability of the various flavors, availability of supplies, and the amounts of ingredients required for each flavor.

She wants to determine the optimal product mix for the Lorimer ice cream.

Let       x₁ = the # of gallons of Chocolate ice cream made

            x₂ = the # of gallons of Vanilla ice cream made

            x₃ = the # of gallons of Strawberry ice cream made

Max Z =    $1.00x₁ + $0.90x₂ + $0.95x₃   

Subject To:

Use your Excel spreadsheet model to answer the following question. Select the answer that best fits what you got. The answer options are not in any particular order.

What is the value of the X2 decision variable at the optimal solution?

Select one:

a. X₂ = 275 gallons

b. X₂ = 220

c. X₂ = 275

d. X₂ = 220 gallons

e. X₂ = 120

f. X₂ = 300 gallons

g. X₂ = 200

h. X₂ = 300

i. X₂ = 200 gallons

j. X₂ = 120 gallons

Choose whether the following statements are true or false.

The null and alternative hypotheses should be written in terms of the sample statistic. TrueFalse

The test statistic is computed assuming that the null hypothesis is true. TrueFalse

The test statistic is usually equal to the sample statistic ?⎯⎯⎯⎯⎯ TrueFalse

The p-value is the probability that the null hypothesis is true. TrueFalse 19. The p-value is the probability that the alternative hypothesis is true. TrueFalse

If the p-value is smaller than the level of significance (?α) then the null hypothesis is rejected. TrueFalse

In 1997 a woman sued a computer keyboard manufacturer, charging that her repetitive stress injuries were caused by the keyboard (Genessey v. Digital Equipment Corporation). The jury awarded about $3.5 million for pain and suffering, but the court then set aside that award as being unreasonable compensation. In making this determination, the court identified a "normative" group of 27 similar cases and specified a reasonable award as one within 2 standard deviations of the mean of the awards in the 27 cases. The 27 award amounts (in thousands of dollars) are in the table below. 39 60 75 115 135 140 149 150 236 290 340 410 600 750 750 750 1050 1100 1139 1150 1200 1200 1250 1578 1700 1825 2000 What is the maximum possible amount that could be awarded under the "2-standard deviations rule"? (Round all intermediate calculations and the answer to three decimal places.)

Zhaoxin needs to successfully complete a coding project that involves complex natural language processing algorithms. Zhaoxin must choose between three different Application Programming Interfaces (API), but is unsure which API is best for the project. Being a Statistician, he decides to collect data, then use random chance to make the final decision. He assigns a probability of 0.45 for PyTorch, 0.25 for Keras, and the rest to TensorFlow. Each API affects Zhaoxin chances of completing the project on time. Zhaoxin will complete the project on-time with a 75% chance if he selects PyTorch, a 55% chance if he selects Keras, and only a 35% chance if he selects TensorFlow.

a) Draw a well-labeled tree diagram to illustrate the above information.

b) What is the probability that Zhaoxin is late and used the TensorFlow API?

c) What is the probability that Zhaoxin is on-time?

d) If Zhaoxin selects Keras as the API, what is the probability that he is on time with the project?

e) If Zhaoxin is late with the project, what is the probability that he selected PyTorch as the API?

f) Is choice of API and project completion independent? Support your answer mathematically.

You have a portfolio with two bonds worth $100 each. Each bond has a 4% probability of defaulting. If the bond defaults it is worth $0. If it does not default it is worth $100. Defaults are independent of each other. What is the 95% VaR of each bond, and of the portfolio?

The proportion of people in a given community who have a certain disease is 0.01. A test is available to diagnose the disease. If a person has the disease, the probability that the test will produce a positive signal is 0.95. If a person does not have the disease, the probability that the test will produce a positive signal is 0.02.

a.Given that the test is positive, what is the probability that the person has the disease?

b.Given that the test is negative, what is the probability that the person does not have the disease?

c.For many medical tests, it is standard procedure to repeat the test when a positive signal is given. Assume that repeated medical tests are independent. What is the probability that the person has the disease given that two independent tests are positive?

6) There are 5 boxes. In each box there are 5 tickets labelled with the numbers 1,2,3,4,5. An experiment is to draw one number at random from each of the five boxes. Calculate the following probabilities using a calculator, but show some work.
a) P(no two numbers alike).
b) P(exactly two alike). (example 11234)
c) P(exactly three alike). (example 11123)
d) P(exactly four alike). (example 11112)
e) P(two pair). (example 11223)
f) P(the number 4 comes up at least once)

Use the Student's t distribution to find t_c for a 0.95 confidence level when the sample is 21. (Round your answer to three decimal places.)

1. The average ACT score for a class of 33 is 21.65, with s=2.83

Covert each of the following to z score:

1. X=19

2. X=25 and

3. X=33

2. The average ACT score for a class of 33 Is 21.65 with s=2.83

What ACT score is 1.5 standard deviations units below the mean?

What score is 2 standard deviation units above the mean?

World Measurement is the global leader in product testing for safety. The recent problem with Chinese-made toy products (for example, Mattel recalled 19 million toys with evidence of lead paint) combined with the global recession has caused a 7% decline in sales and 12% in net profits. The president of the company, Lewis Jacobs, is convinced that he must get concessions from the workers if World Measurement is to compete effectively with increasing foreign competition. In particular, Jacobs is displeased with the cost of employee benefits. He doesn't mind conceding a competitive wage increase (maximum 3%), but he wants the total compensation package to cost 3% less. The current costs are shown in Exhibit 1 (attached). Your assistant has surveyed other companies that are obtaining concessions from employees. You also have data from a consulting firm that indicates employee preferences for different forms of benefits (see Exhibit 2 attached). Based on all this information, you have two possible concession packages that you can propose, labeled "Option 1" and "Option 2" (see Exhibit 3 attached). Please analyze and answer each of the questions below. It is not necessary for you to type the question itself. Your assignment should be 3-4 pages long, double-spaced, using 12-point font, excluding cover page, attachments, etc. 1. Cost out these packages given the data in Exhibit 1 and the information obtained from various insurance carriers and other information sources (see Exhibit 4 attached). 2. Which package should you recommend to Jacobs? Why? 3. Which of these strategies do you think will require less input from employees in terms of their reactions? Why? Exhibit 1: Current Compensation Costs Average yearly wage $27,290.00 Average hourly wage 13.12 Dollar value of yearly benefits, per employee 16,904.00 Total compensation (wages plus benefits) $44,194.00 Benefits (by Category) Dollar Cost/Employee/Year 1. Legally required payments (employer’s share): a. FICA taxes $2,088.00 b. Unemployment compensation 434.00 c. Workers’ compensation 546.00 2. Pension, insurance, etc. (employer’s share): a. Pension plan premiums/pension payments 1,460.00 b. Life insurance and health insurance 427.00 c. Health insurance 4,000.00 c. Short-term disability 83.00 d. Salary continuation/long-term disability 57.00 e. Dental insurance 350.00 f. Discounts on goods/services purchased from company by employees 27.00 g. Miscellaneous payments (separation or termination pay moving expenses, etc.) 124.00 3. Paid rest periods, lunch periods, wash-up time, clothes- change time, get ready time, etc. (60 minutes/day) 3410.00 4. Payments for time not worked: a. Paid vacations/payments in lieu of vacation (16 days per year average) 1,680.00 b. Payments for holidays not worked (9 days) 945.00 c. Paid sick leave (10 days maximum) 1050.00 d. Payments for state or national guard duty, jury duty, bereavement pay, voting pay allowance 66.00 5. Other items: a. Profit sharing payments 0.00 b. Contributions to employee thrift plans 71.00 c. Christmas or other special bonuses, service awards, suggestion awards, etc. 0.00 d. Employee education expenditures (tuition reimbursement, etc.) 40.00 e. Special wage payments ordered by courts, payments to union stewards, etc. 46.00 Total $16,904.00 Exhibit 2: Benefit Preferences Benefit Type/Method of Administration Importance to Workers Pensions 87 Health insurance 86 Life insurance 79 Paid vacation 82 Holidays 82 Long-term disability 72 Paid sick leave 70 Short-term disability 69 Paid rest periods, lunch periods, etc. 55 Dental insurance 51 Christmas bonuses 31 Profit sharing 21 Education expenditures 15 Contributions to thrift plans 15 Discount on goods 5 Fair treatment in administration 100 Note: 0 = unimportant; 100 = extremely important Exhibit 3: Two Possible Packages for Cutting Benefit Costs Option 1: Implement copay for benefits: - Pension plan ($25.00 per month) - Life insurance premium ($10.00 per month) - Health insurance premiums ($50.00 per month) - Dental insurance ($10.00 per month) - Short-term and long-term disability insurance ($7.50 per month) Reduction of Benefits - Eliminate 10-minute paid break (workers leave work 10 minutes earlier) - Eliminate one paid holiday per year - Eliminate two sick days per year Option 2: Improved claims processing: - Unemployment compensation - Workers’ compensation - Short- and long-term disability insurance Increase deductible from $500 to $1,000 on health insurance Implement probationary periods: - 6 months’ probationary period on health insurance - 1 year probationary period on dental insurance Implement probationary period of 1 year on dental insurance Implement copay for benefits: - Health insurance - $50.00 per month - Dental insurance - $10.00 per month - Life insurance - $10.00 per month - Short- and long-term disability insurance - $5.00 per month Reduction of benefits: - Eliminate payments to thrift plan - Eliminate two paid holidays per year - Eliminate tuition reimbursement Exhibit 4: Analysis of Cost Implications Cost Saving Strategy: Copay - Dollar-for-dollar savings equal to amount of copay Deductible: - Health insurance – 15% savings of benefit cost Required probationary periods: - Health insurance – 5% savings of benefit cost - Dental insurance – 10% savings of benefit cost Improved claims processing: - Unemployment compensation – 8% of benefit cost - Workers’ compensation – 3% of benefit cost - Short-term and long-term disability – 1% of benefit cost

How much time does an algorithm take to solve a problem of size n if this algorithm uses 2n2 + 2n operations, each requiring 10-8 seconds, with these values of n?

a) 10:

b) 20:

c) 50:

d) 100

Descriptive Statistics and Graphical Displays

Valencia Orange Price Comparison

You have been hired as a consultant to determine who ABC Grocery Store should be ordering Valencia Oranges from.

To: Statistician

From: ABC Grocery Store

Please advise us on which company to use as our orange distributor. Three highly recommended distributors have provided us with statistical data on the weekly prices for one load of Valencia oranges per week for a ten-week period last year. Prices fluctuate according to availability, and we would like to use the company with the lowest overall price and the least amount of fluctuation. We would like your written report showing your results and a detailed recommendation as to which company we should choose.

Thank you.

Here are the prices, listed as price in dollars per crate:

You must type in and analyze the data for each company.

Helpful directions:

1. Analyze the data for each company: frequency, relative frequency, mean, median,******* (ONLY complete the mode, standard deviation and range because below I am going to list my answers for the frequency, relative frequency, mean and median)
2. You need to decide which statistics to compare to determine the overall lowest price and the least fluctuation. Create and include at least two charts that will be useful to best support your conclusions.
3. Write a brief informative letter in response to the request from ABC Grocery answering their request. Be sure to include:
   1. A very detailed explanation of the data and the conclusions you came to. You should use the statistics you calculated to make this decision.
   2. Charts to support your explanation.
4. Attach copies of the Excel pages or embed the Excel work in your letter of response.