Statistics professor offers two midterm exams

Reference no: EM131817022

Suppose a statistics professor offers two midterm exams, each worth 100 points. A student plans to do a lot of traveling during the semester for job interviews, and asks if she can miss one of the midterms. The professor gives her the option of taking both midterms as scheduled, or taking just one midterm and doubling the score.

a. Which of the random variables 2X₁ and X₁ + X₂ represents the student's score if she takes both midterms? Which represents her score if she takes just one midterm and doubles the score?

b. If the student takes both midterms, and does somewhat worse than usual on one, she may do somewhat better than usual on the other, so that her combined midterm score isn't too bad. If she takes just one midterm, and does somewhat worse than usual, then the doubled score is also worse than usual; if she does somewhat better, then the doubled score is also better than usual. In which case is there more of a tendency for unusually low or high scores-if she takes both midterms, or if she takes just one midterm and doubles the score?

c. This is a fairly average student, and her exam performance Xi is a random variable with mean 80. Find the mean of 2X₁ and find the mean of X₁ + X₂.

d. Are the means you found in part (c) equal? If not, tell which is larger and why.

e. Suppose a student's exam performance Xi has standard deviation 5. Find the standard deviation of 2X₁ and find the standard deviation of X₁ + X₂, according to formulas on page 282 and 284.

f. Are the standard deviations you found in part (e) equal? If not, tell which is larger and why.

g. To find the standard deviation of X₁ + X₂ in part (e), one must assume that a student's scores X₁ and X₂ on the first and second midterm exams are independent. Is this a reasonable assumption?

Reference no: EM131817022

Questions Cloud

Discussion of the chosen company structure and products : HI5019 STRATEGIC INFORMATION SYSTEMS Assignment - Literature Review. Discussion of the chosen company's structure, products and services under consideration

How is the religion responding to challenges in modern world : How is this religion responding to challenges (e.g., the rise of critical and scientific methodologies) in the modern world?

How the world health organization helps to provide care : Compare a foreign country's quality of care to the United States' quality of care.

Discuss what percentage of the throughput time was spent : What percentage of the throughput time was spent on non-value-added activities

Statistics professor offers two midterm exams : Suppose a statistics professor offers two midterm exams, each worth 100 points. A student plans to do a lot of traveling during the semester for job interviews

Weights in kilograms of boys at the start : Find the z-score for each of the following weights, and characterize it as "very light," "somewhat light," "somewhat heavy," or "very heavy."

Do you believe that what you found is actionable in courts : You do not need to describe the item that in fact raised your concern but you certainly may. There is no item you might find on me that you cannot discuss.

Information about the tails of the normal curve : Information about the tails of the normal curve asserts that the probability is 0.05 that a standardized score z falls below 1.645, and 0.05 that z falls above

Probability that the mean verbal sat score : For each of the following situations, tell whether the two probabilities should be equal:

User Account

All Pages