In the table below, there are test scores from a dozen students. The test was worth 200 points. The scores in the table are the # of points out of 200. Letter grades will be assigned using the standard grade boundaries given below.

You will need to create a new Excel file for this assignment.

1. Create a worksheet with the columns of student names and scores as shown above.
2. Add a column to the right of Test Score labeled “Percentage”
3. Add a column to the right of Percentage labeled “Letter grade”
4. Using absolute addressing, calculate the corresponding percentage score for each student. You must utilize absolute addressing in this formula. (hint – put the total possible score in one separate cell someplace in your worksheet and use it for the first student, then copy and paste).
5. Use the AVERAGE function to calculate the average percentage and display with a label of “Average Percentage”.
6. Use the MAX function to calculate the highest percentage score and display with a label of “Maximum Percentage.”
7. Using VLOOKUP, determine and display the letter grade for each student.

The numbers 1,6,15,20,15,6,1 are the coefficients of the binominal expansion (p+q)^6. Use the normal quantile plot method to show that these numbers are close to a normal distribution.

Majesty Video Production Inc. wants the mean length of its advertisements to be 26 seconds. Assume the distribution of ad length follows the normal distribution with a population standard deviation of 2 seconds. Suppose we select a sample of 14 ads produced by Majesty. What can we say about the shape of the distribution of the sample mean time? What is the standard error of the mean time? (Round your answer to 2 decimal places.) What percent of the sample means will be greater than 27.25 seconds? (Round your z values and final answers to 2 decimal places.) What percent of the sample means will be greater than 24.50 seconds? (Round your z values and final answers to 2 decimal places.) What percent of the sample means will be greater than 24.50 but less than 27.25 seconds? (Round your z values and final answers to 2 decimal places.)

13) A logging truck sales representative can contact either one or two potential buyers per day with probabilities of 0.25 and 0.75, respectively. Each contact will result in either no sale or a $75,000 sale with probabilities of 0.85 and 0.15, respectively(hint: start with a tree diagram)

a) Show the probability distribution of daily sales.

b) What is the expected value of daily sales?

c) What is the standard deviation of daily sales?

Two standardized​ tests, test A and test​ B, use very different scales. Assume that in one year the distribution of scores on test A can be modeled by N(1000, 75) and scores on test B can be modeled by N(27, 4). If an applicant to a university has taken test A and scored 1220 and another student has taken test B and scored 39​, compare these​ students' scores using​ z-values. Which one has a higher relative​ score? Explain.

For 300 trading​ days, the daily closing price of a stock​ (in $) is well modeled by a Normal model with mean ​$196.38 and standard deviation $7.13.

According to this ​model, what is the probability that on a randomly selected day in this period the stock price closed as follows.

​a) above ​$203.51?

​b) below ​$210.64​?

​c) between ​$182.12 and ​$210.64?

​d) Which would be more​ unusual, a day on which the stock price closed above ​$206 or below ​$180?

IRS data indicates that the tax refunds it issued this year follow the normal distribution with μ = 1,200 and σ = 200. Based on this information calculate the following probabilities.

1. Probability of selecting a tax return, the refund for which will fall between $1,170 and $1,200:
   
   
   
2. Probability of selecting a tax return, the refund for which will be less than $1,406:
   
   
   
3. Probability of selecting a tax return, the refund for which will be more than $1,598:
   
   
   
4. Probability of selecting a tax return, the refund for which will fall between $1,132 and $1,354:

17. Why should you avoid contrasting red and green as colors on a graph for presentations?

18. Why would you use a semilogarithmic scale line graph instead of an arithmetic scale line graph?

19. Construct a pie chart using your computer. Word works very well for doing this. Use any information you like but it must contain at least 5 sections. It must be original! Do not use the example within Word (i.e. Sales) or from a website. Attach or copy and paste below.

A vehicle quality survey asked new owners a variety of questions about their recently purchased automobile. One question asked for the owner’s rating of the vehicle using categorical responses of average, outstanding, and exceptional. Another question asked for the owner’s education level with the categorical responses some high school, high school graduate, some college, and college graduate. Assume the sample data below are for  owners who had recently purchased an automobile.

a. Use a  level of significance and a test of independence to determine if a new owner's vehicle quality rating is independent of the owner's education.

Compute the value of the  test statistic (to 2 decimals).

The -value is - Select your answer -between .01 and .025between .025 and .05between .05 and .10greater than .10less than .01Item 2

What is your conclusion?

- Select your answer -Cannot concludeConcludeItem 3 that the quality rating is not independent of the education of the owner.

b. Use the overall percentage of average, outstanding, and exceptional ratings to comment upon how new owners rate the quality of their recently purchased automobiles.

New owners - Select your answer -do not appearappearItem 7 to be satisfied with the recent purchase of their automobile.   of owners rated their automobile as Outstanding or Exceptional.

A survey by KRC Research for U.S. News reported that 40% of people

     plan to spend more on eating out after they retire. Suppose a random sample of 20   

     people are selected and the process follows a binomial distribution, with p = 0.40

a. What is the expected value and standard deviation of the people in the sample who

      plan to spend more on eating out after they retire.

b. What is the probability that 8 or fewer in the sample indicate that they plan to spend

      more on eating out after retirement?

c. What is the probability that at least 9 people (i.e. 9 or more) in the sample indicate

      that they plan to spend more on eating out after retirement?

Let X₁, X₂,..., X_nbe independent and identically distributed exponential random variables with parameter λ .

a) Compute P{max(X₁, X₂,..., X_n) ≤ x} and find the pdf of Y = max(X₁, X₂,..., X_n).
b) Compute P{min(X₁, X₂,..., X_n) ≤ x} and find the pdf of Z = min(X₁, X₂,..., X_n).
c) Compute E(Y) and E(Z).

A Pew Research Center survey asked respondents if they would rather live in a place with a slower pace of life or a place with a faster pace of life. The survey also asked the respondent’s gender. Consider the following sample data.

a. Is the preferred pace of life independent of gender? Using a  level of significance, what is the -value?

Compute the value of the  test statistic (to 3 decimals).

The -value is - Select your answer -between .01 and .025between .025 and .05between .05 and .10greater than .10less than .01Item 2

What is your conclusion?

- Select your answer -Cannot concludeConcludeItem 3 that the preferred pace of life is not independent of gender.

b. What are the percentage responses for each gender (to 1 decimal)?

Discuss any differences between the preferences of men and women.

- Select your answer -Men onlyWomen onlyBoth men and womenItem 10 prefer a slower pace of life. Women have a higher preference for a  - Select your answer -slowerfasterItem 11 pace of life, while men have a higher preference for a - Select your answer -slowerfasterItem 12 pace of life.

A survey found that​ women's heights are normally distributed with mean 62.4 in. and standard deviation 2.1 in. The survey also found that​ men's heights are normally distributed with mean 67.3 in. and standard deviation 3.1 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 56 in. and a maximum of 63 in.

1.Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement​ park?

2.Find the percentage of women meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement​ park?

Logistic regression predicts a 1._____________, 2._____________, 3.______________from one or more categorical or continuous predictor variables.

When σ is unknown and the sample is of size n ≥ 30, there are two methods for computing confidence intervals for μ.

Method 1: Use the Student's t distribution with d.f. = n − 1.
This is the method used in the text. It is widely employed in statistical studies. Also, most statistical software packages use this method.

Method 2: When n ≥ 30, use the sample standard deviation s as an estimate for σ, and then use the standard normal distribution.
This method is based on the fact that for large samples, s is a fairly good approximation for σ. Also, for large n, the critical values for the Student's t distribution approach those of the standard normal distribution.

Consider a random sample of size n = 41, with sample mean x = 46.0 and sample standard deviation s = 4.6.

(a) Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

(b) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal.

(c) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution?

Yes. The respective intervals based on the t distribution are shorter.

Yes. The respective intervals based on the t distribution are longer.    

No. The respective intervals based on the t distribution are shorter.

No. The respective intervals based on the t distribution are longer.

(d) Now consider a sample size of 81. Compute 90%, 95%, and 99% confidence intervals for μ using Method 1 with a Student's t distribution. Round endpoints to two digits after the decimal.

(e) Compute 90%, 95%, and 99% confidence intervals for μ using Method 2 with the standard normal distribution. Use s as an estimate for σ. Round endpoints to two digits after the decimal.

(f) Compare intervals for the two methods. Would you say that confidence intervals using a Student's t distribution are more conservative in the sense that they tend to be longer than intervals based on the standard normal distribution?

No. The respective intervals based on the t distribution are longer.

Yes. The respective intervals based on the t distribution are shorter.   

No. The respective intervals based on the t distribution are shorter.

Yes. The respective intervals based on the t distribution are longer.

With increased sample size, do the two methods give respective confidence intervals that are more similar?

As the sample size increases, the difference between the two methods remains constant.

As the sample size increases, the difference between the two methods becomes greater.    

As the sample size increases, the difference between the two methods is less pronounced.