Suppose calls to a software support centre over a given period of time occur randomly, independently...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Suppose calls to a software support centre over a given period of time occur randomly, independently and at a homogeneous rate of calls per hour. In solving for the questions below set last digit of your student number + 10, for example if your student number is 20327203 then the last digit is 3 and A = 10 +3 = 13 calls per hour. Note: in this question I ask you to use R to solve for probabilities. To get full marks you need to include the probability expression in terms of the random variable, as well as its simplification and then the probability value obtained from R. For example, if you are asked to solve for the probability that we observe less than 2 calls in an hour your solution should include the following: >ppois (1,13) P(X <2) = P(X = 0) + P(X = 1) = e13 [1] 3.164461e-05 [130 131] a) (2) In this question we are assuming that the average number of calls received is homogenous i.e the same regardless of the time of day or day of week etc. Explain, in your own words, whether this assumption is valid. a) (2) Use R to solve for the probability that there are less than 4 calls in a 30-minute period. b) (2) Use R to solve for the probability that there are at least 10 calls received in a 1-hour period. c) (2) Use R to solve for the probability that exactly 25 calls are received in a two-hour interval. d) (2) The support centre would like to track the volume of calls. If in a two-hour interval more than 35 calls are received the support centre calls this a "stressful event". Use R to solve for the probability that in any particular two-hour interval a "stressful event" occurs. e) (3) Assume that the day is considered to run from 8am to 8pm i.e 12 hours long, or 6 two-hour intervals. Use R to solve for the probability that among the 6 two-hour intervals less than 2 are labeled as "stressful event". f) (2) Assume that the day is considered to run from 8am to 8pm i.e 12 hours long, or 6 two-hour intervals. In addition, assume that the support centre is open Monday to Friday each week. Assuming we just started a new week i.e Monday at 8am, use R to solve for the probability that the first "stressful event" occurs after the 12th two-hour interval that passes. Suppose calls to a software support centre over a given period of time occur randomly, independently and at a homogeneous rate of calls per hour. In solving for the questions below set last digit of your student number + 10, for example if your student number is 20327203 then the last digit is 3 and A = 10 +3 = 13 calls per hour. Note: in this question I ask you to use R to solve for probabilities. To get full marks you need to include the probability expression in terms of the random variable, as well as its simplification and then the probability value obtained from R. For example, if you are asked to solve for the probability that we observe less than 2 calls in an hour your solution should include the following: >ppois (1,13) P(X <2) = P(X = 0) + P(X = 1) = e13 [1] 3.164461e-05 [130 131] a) (2) In this question we are assuming that the average number of calls received is homogenous i.e the same regardless of the time of day or day of week etc. Explain, in your own words, whether this assumption is valid. a) (2) Use R to solve for the probability that there are less than 4 calls in a 30-minute period. b) (2) Use R to solve for the probability that there are at least 10 calls received in a 1-hour period. c) (2) Use R to solve for the probability that exactly 25 calls are received in a two-hour interval. d) (2) The support centre would like to track the volume of calls. If in a two-hour interval more than 35 calls are received the support centre calls this a "stressful event". Use R to solve for the probability that in any particular two-hour interval a "stressful event" occurs. e) (3) Assume that the day is considered to run from 8am to 8pm i.e 12 hours long, or 6 two-hour intervals. Use R to solve for the probability that among the 6 two-hour intervals less than 2 are labeled as "stressful event". f) (2) Assume that the day is considered to run from 8am to 8pm i.e 12 hours long, or 6 two-hour intervals. In addition, assume that the support centre is open Monday to Friday each week. Assuming we just started a new week i.e Monday at 8am, use R to solve for the probability that the first "stressful event" occurs after the 12th two-hour interval that passes.
Expert Answer:
Related Book For
Statistics The Exploration & Analysis Of Data
ISBN: 9780840058010
7th Edition
Authors: Roxy Peck, Jay L. Devore
Posted Date:
Students also viewed these computer network questions
-
can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...
-
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
-
The price of a stock is $55. A put option written on this stock with a strike price of $48.8 is quoted at $7.2. One option contracts covers 100 underlying shares. A trader enters a short position in...
-
* For the network in Fig. 8.89, find i(t) for t > 0. 5 20 1 H t-0 100 v (
-
In a Python class, how do you hide an attribute from code outside the class?
-
(a) A gallon of gasoline contains about \(1.4 \times 10^{8} \mathrm{~J}\) of chemical energy. A car consumes this amount of gasoline in approximately \(30 \mathrm{~min}\) when cruising along a...
-
Lisali Company gathered the following information related to inventory that it owned on December 31, 2011: Historical cost ......... $100,000 Replacement cost ....... 95,000 Net realizable value...
-
16. Let a1, a2, 17. a <0 is: (a) 22 be in H.P. with a = 5 and a20 = 25. The least positive integer n for which " (b) 23 Sum of the series rlog. r=1 (c) 24 (d) 25 r+1 + is: r
-
On Juans twenty-sixth birthday, he invested $7,500 in a retirement account. Each year thereafter, he deposited 8 percent more than the previous deposit. The account paid annual compound interest of 5...
-
Outline the criteria that must be met in order for a liability limitation agreement between a company and its auditor to be effective.
-
Explain briefly what is meant by an accounting system.
-
Live Nation operates music venues, provides management services to music artists, and promotes more than 26,000 live music events annually. The company acquired House of Blues, merged with...
-
Explain briefly the importance of the following cases to the development of auditors responsibilities: (i) Re London and General Bank (No. 2) [1895]; (ii) Re Kingston Cotton Mill Co. Ltd (No. 2)...
-
The use of generic class of items can be used when the precise identity of items cannot be ascertained. T or F
-
Describe the process of deciding if a new business is a good risk. Include a discussion of the market conditions and the overall economic conditions that would create an optimal situation for an...
-
g(x) = x 5 5x 6 a. Show that g(x) = 0 has a root, , between x = 1 and x = 2. b. Show that the equation g(x) = 0 can be written as x = (px + q) 1/r , where p, q and r are integers to be found. The...
-
Use a virial expansion approach to determine the first few nontrivial order contributions to the pair correlation function \(g(r)\) in \(d\) dimensions. Show that the pair correlation function is of...
-
For the particular case of hard spheres, the pressure in the virial equation of state is determined by evaluating the pair correlation function at contact. Write the pair correlation function as...
-
(a) For a dilute gas, the pair correlation function \(g(r)\) may be approximated as \[g(r) \simeq \exp \{-u(r) / k T\}\] Show that, under this approximation, the virial equation of state (10.7.11)...
Study smarter with the SolutionInn App