1. Suppose you own a fish restaurant and you believe that the demand for sea bass is distributed normally (that is, follows the bell-shaped curve) with a mean of 12 pounds and a standard deviation of 3.2. In summary, we express this as N(12,3.2).

   1a. The notation N(12,3.2) means that

   		The mean (average) is 3.2 and the standard deviation is 12
   		The mean is 12 and the standard deviation is 3.2 and the data follows a bell shape curve
   		The mean is 12 and the standard deviation is 3.2 and the data does not follow a bell shape curve

10 points

Question 2

1. What is the z-score for 20 pounds of sea bass? You find the z-score by calculating (x-mean)/standard deviation

   		0.0062
   		2.50
   		0.9938
   		0.25

10 points

Question 3

1. The number inside Table A associated with 2.50 is

   		2.50
   		0.0062
   		0.9938
   		0.25

10 points

Question 4

1. The number in the table represents that area to the

   		Right
   		Left

10 points

Question 5

1. So 0.9938 is the area associated with a Z score of

   		2.50 or more
   		2.50 or less

10 points

Question 6

1. The probability that you will need 20 pounds or more of sea bass is

   		0.25
   		0.0062
   		0.9938
   		2.50

10 points

Question 7

1. What is the z-score for 15 pounds of sea bass

   		0.94
   		0.8264
   		0.06
   		-0.94

10 points

Question 8

1. What is the number inside table A associated with 0.94

   		0.8264
   		0.1736
   		0.94

10 points

Question 9

1. So 0.8264 is the area associated with a Z score of

   		0.94 or less
   		0.94 or more

10 points

Question 10

1. The probability that you will need 15 pounds of sea bass or less is

   		0.1736
   		0.94
   		0.8264

10 points

Question 11

1. What is the probability that you will need between 15 and 20 pounds of sea bass

   		0.94
   		0.8264
   		0.1674

10 points

Question 12

1. What is the z-score associated with the 95th percentile of the standard normal curve

   		0.95
   		1.65
   		1.28

10 points

Question 13

1. How many pounds of sea bass are needed for the 95th percentile of sea bass demand

   		1.65
   		7.28
   		17.28

"You ask students to identify European countries on a map. On average students will identify 10% of the countries correctly. A similar test for US states indicates a 45% success rate. Asking students to identify 7 European countries and 3 US states, what is the chance that students will correctly identify at least 50% of the countries/states?"

"You have a set of 100 batteries. 13 of these batteries are defective. Testing 25 batteries, what is the probability to find 3 or more of the 25 batteries failing?"

1. The true, unobserved population mean commute distance among all urban planners working in the Melbourne Metropolitan Area (μ) is 22km, with σ=15. You conduct a survey of 144 planners and find that the sample means commute distance (X-bar) is 25km (12 points).

1. Describe two possible sources of bias that could have produced this high estimate? (4 points)
2. Is this sample mean impossible if no bias is introduced from your sampling process or survey questions? Why or why not? (4 points)
3. Presuming that no bias is introduced by your sampling and survey, what is the probability that you will draw this sample? Show your work. (4 points)

Genetic theory predicts that, in the second generation of a cross of sweet pea plants, flowers will be either red or white, with each plant having a 25% chance of producing red flowers. Flower colours of separate plants are independent. Let X be the number of plants with red flowers out of 20 plants selected at random from the second generation of this cross. (a) What is the probability distribution of X? [3] (b) Calculate: (i) the mean and standard deviation of X. [3] (ii) P( X > 8) [2] (iii) P( 4 ≤ X ≤ 10) [2] (c) If only 3 of the 20 plants had red flowers, would this be an unusual sample? Calculate a probability and use it to justify your answer

Problem 4: A large firm uses three different types (A, B, and C) of raw materials to manufacture its product. Previous records show that 25% of the manufactured products are produced using material A, 50% using material B, and 25% using material C. If it is known that 5% of the product made with material A are defective, 2% made with material B are defective, and 5% made with C are defective.
What is the probability that a product selected at random from this firm will be defective?
If a product selected at random from this firm is found to be defective, what is the probability that it was made from material A.

Question 2

Frasers Logistics operates a large fleet of trucks that transport goods on behalf of their clients. The trucks undergo regular scheduled maintenance as well as unscheduled maintenance when a problem occurs.   Data about the maintenance expense is collected continuously and recorded by the admin staff of Frasers.   Frasers do believe in updating their fleet of trucks on a continuous basis and hence has trucks in operation of various ages.   They suspect that both the age of the truck as well as the distance covered in km in a particular year will have an impact on the maintenance costs of the trucks. The data for a particular size truck has been collected and is shown in the table below.

The Expense column reflects the full maintenance expense for that particular truck during the past financial year, the Distance column reflects the distance in km that the truck covered in the past financial year and the Age column reflects the age of the truck.

Use the data in the sheet named “Frasers” and use Excel and the Data Analysis add-in to perform linear regression analysis on the data to determine whether direct distance travelled (K) or age (A) or both should be used for estimating future maintenance expenditure. Specifically answer the following questions:

1. Decide which linear regression model (with distance travelled (K) or age (A) or both as independent variable) is the better model and motivate your selection.

The remaining answers must be based on the model that you have selected.

2. What is the total variation in “Expense” that is explained by the independent variable(s) that you have selected.
3. Is the overall regression model statistically significant? Test at the 5% level of significance using the model that you have selected in a. For this test formulate the appropriate null and alternative hypothesis, determine the region of acceptance, use the appropriate test statistic and draw the statistical and management conclusions.
4. Is the distance travelled (K) variable significant at the 5% level of significance? For this test use the model that you have selected in a. and formulate the appropriate null and alternative hypothesis, determine the region of acceptance, use the appropriate test statistic and draw the statistical and management conclusions.
5. Interpret the intercept of the regression equation.
6. Write down the linear regression equation in algebraic format using E for expense, K for the distance travelled and A for the age of the truck.

The expected number of births at a rural hospital is one per day. Assume that births occur independently and at a constant rate.

1. Use R to the draw the pmf of the number of births per day at this hospital.

2. Find the probability of observing at least 3 births in a day.

3. Find the probability of observing at most 5 births in a week.

4. At a larger hospital, the expected number of births per day is 17.4. Assume that births occur independently and at a constant rate. On average, how long do we have to wait until a birth at this hospital?

5. What is the distribution of the total number of births per day at both of these two hospitals (the sum of births at each of the hospitals)? State any assumptions that you are making.

Test the hypothesis using the​ P-value approach. Be sure to verify the requirements of the test.

Upper H 0 : p equals 0.58 versus Upper H 1 : p less than 0.58H0: p=0.58 versus H1: p<0.58

n equals 150 comma x equals 81 comma alpha equals 0.01n=150, x=81, α=0.01

Is

np 0 left parenthesis 1 minus p 0 right parenthesis greater than or equals 10np01−p0≥10​?

No

Yes

it is claimed that the following data comes from a Poisson distribution with mean 5.

test the claim at a 0.01 level of significance

Please answer the following: United Dairies, Inc., supplies milk to several independent grocers throughout Dade County, Florida. Managers at United Dairies want to develop a forecast of the number of half gallons of milk sold per week. Sales data for the past 12 weeks are:

1. Compute four-week and five-week moving averages for the time series.

1. 1. Compute the MSE for the four-week and five-week moving average forecasts.
   2. What appears to be the best number of weeks of past data (three, four, or five) to use in the moving average computation? The MSE for three weeks is 23527.78
2. Show the exponential smoothing forecasts using α = 0.1.
   1. Applying the MSE measure of forecast accuracy, would you prefer a smoothing constant of α=0.1 or α= 0.2 for the United Dairies sales time series?
   2. Are the results the same if you apply MAE as the measure of accuracy?
   3. What are the results if MAPE is used?
3. Use exponential smoothing with a α = 0.4 to develop a forecast of demand for week 13. What is the resulting MSE?

PLEASE USE EXCEL AND ANSWER EACH PART OF THE QUESTION. THANKS !

ANSWER- THAT'S WHAT I GOT SO FAR:

One of the items that businesses would like to be able to test is whether or not a change they make to their procedures is effective. Remember that when you create a hypothesis and then test it, you have to take into consideration that some variance between what you expect and what you collect as actual data is because of random chance. However, if the difference between what you expect and what you collect is large enough, you can more readily say that the variance is at least in part because of some other thing that you have done, such as a change in procedure.

For this submission, you will watch a video about the Chi-square test. This test looks for variations between expected and actual data and applies a relatively simple mathematical calculation to determine whether you are looking at random chance or if the variance can be attributed to a variable that you are testing for.

Imagine that a company wants to test whether it is a better idea to assign each sales representative to a defined territory or allow him or her to work without a defined territory. The company expects their sales reps to sell the same number of widgets each month, no matter where they work. The company creates a null and alternate hypothesis to test sales from defined territory sales versus open sales.

One of the best ways to test a hypothesis is through a Chi-square test of a null hypothesis. A null hypothesis looks for there to be no relationship between two items. Therefore, the company creates the following null hypothesis to test: There is no relationship between the amount of sales that a representative makes and the type of territory (defined or open) that a representative works in. The alternate hypothesis would be the following: There is a relationship between the kind of sales territory a sale representative has (defined or open) and the amount of sales he or she makes during a month.

Step 1:

Watch this video.

Step 2:

Use the following data to conduct a Chi-square test for each region of the company in the same manner you viewed in the video:

Step 3:

Write an 800–1,000-word essay, utilizing APA formatting, to discuss the following:

• Describe why hypothesis testing is important to businesses.
• Report your findings from each Chi-square test that you conducted.

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that σ is known to be $1.94 per 100 pounds.

(a) Find a 90% confidence interval for the population mean price (per 100 pounds) that farmers in this region get for their watermelon crop. What is the margin of error? (Round your answers to two decimal places.)

(b) Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.45 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)
farming regions

(c) A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error? Hint: 1 ton is 2000 pounds. (Round your answers to two decimal places.)

In a city, the racial make up is 68% White, 24% Black, 5% Asian and the remainder are classified as Other. A report on traffic stops by police officers in this city is being used to determine if the racial makeup of the motorists stopped reflect the racial makeup of the city. The race of drivers stopped by police officers over a 4 month period is recorded in the table. Determine if there is sufficient evidence to warrant the claim that the racial makeup of drivers in traffic stops significantly differs from the city's racial makeup.

R

ace White Black Asian Other Drivers 896 399 68 57 At the 0.025 significance level, test the claim that the racial distribution of drivers stopped in traffic stops conforms to the city's distribution of races.

The test statistic

is χ2=

The p-value is T

he conclusion is A. There is sufficient evidence to claim the racial makeup of drivers pulled over in traffic stops does not reflect the racial makeup of the city. B. There is not sufficient evidence to claim the racial makeup of drivers pulled over in traffic stops does not reflect the racial makeup of the city

Question 3: A freshman class consists of 6 students, 3 of which are girls. The class needs to select a committee of 2 to represent them in the student senate.

(1) Write the sample space of this experiment.
(2) Calculate the probability of a committee of two boys. (3) Calculate the probability of one boy and one girl.