Reference no: EM131238593
Refer to the "Cars at an intersection" example in Section 4.1.1 to answer the questions below.
(a) The data for this problem were collected between 3:25p.m. and 4:05p.m. on a non-holiday weekday. Ideally, it would also be important to understand the traffic patterns for other time periods. The number of cars stopped at the intersection is likely to vary due to factors such as time of day, day of the week, whether school is in session, and so forth. Discuss how these factors could have been accounted for in designing this study.
(b) Are the observations truly independent? If not, discuss what assumptions must be made to use the Poisson distribution for this problem.
(c) The lengths of vehicles and the distances between stopped vehicles vary. For the purpose of this problem, suppose all vehicles are 14 feet long with a distance between cars of 4 feet when stopped at the intersection. This suggests that 9 vehicles (150/18 = 8.3) or more will at least partially block the fire station's driveway. Using a Poisson distribution, estimate the probability this will happen for one stoplight cycle. Considering part (a), what caveats need to be placed on the interpretation of this probability?
(d) Using the probability from part (c), estimate the probability that the fire station's driveway is at least partially blocked at least once over 60 cycles of the light (roughly one hour). Use the binomial distribution to help answer this problem.
|
Distribution of individual failure times
: Would it be reasonable to assume that the distribution of individual failure times should be roughly normal? Would it be reasonable to assume that the distribution of sample means should be roughly normal?
|
|
What would be the total cost recorded for job-c
: Managerial Accounting Determine breakeven total volume of sales and sales volume for each product and determine sales volume and sales revenue for the company to earn Br500,000 profit after 30% profit tax.
|
|
Number of times a high school student
: Suppose that the number of times a high school student says "like" in a sentence is approximately normally distributed with a mean of 4 and a standard deviation of .5.
|
|
Draw the directed graph of relation
: Given the set A = {1, 2, 3} and the set S = {(x, y) | x and y in A}. Consider the relation ≤ defined on S as follows: ((x1, y1) ≤ (x2, y2) if x1 ≤ x2 and y1 ≤ y2. Draw the directed graph of this relation. Show that it is a partial order. Explain why ..
|
|
Are the observations truly independent
: Using the probability from part (c), estimate the probability that the fire station's driveway is at least partially blocked at least once over 60 cycles of the light (roughly one hour). Use the binomial distribution to help answer this problem.
|
|
Example of an equivalence relation
: Give an example of an equivalence relation that is defined on a particular set. State what the set is and how the equivalence relation is defined. Show that the relation satisfies the three properties required of equivalence relations.
|
|
How does participation in and patronage of theatre reflect
: Your assignment is to write a letter to the President and Board of Trustees outlining the benefits of studying theatre, keeping our core values in mind. What have you learned about the theatre this term that could help you communicate the value of..
|
|
Compare the results to those from zeroinflated poisson model
: what is the difference in assumptions between the two models regarding the source of zero counts? (Note that the coefficients in the probability model estimate P(Y > 0|z), but predict(..., type = "prob") returns P(Y = 0|z).)
|
|
Compare the number of successful skin grafts
: A plastic surgeon wants to compare the number of successful skin grafts in her series of burn patients with the number in other burn patients. A literature survey indicates that approximately 30% of the grafts become infected but that 80% survive.
|