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Essay

1. Use the background information below to create the essay.

Case Study

Scenario

Land and Agua Insurance Company has a call center in Tempe, Arizona. The business

was originally established in Phoenix, Arizona in 1972 as a small business, and it has

grown with the population of the area. The insurance company specializes in bundling

insurance for cars, off-road vehicles, and watercraft (e.g., jet skis and boats). The

company has 150,000 clients in Arizona.

Marjorie Jones, Vice President of Operations, is concerned about customer complaints

and the amount of time representatives are taking to resolve the calls. You are part of

the team investigating the data to determine the probabilities of errors and call times.

Ms. Jones also wants to understand the approximate range around the average for call

times.

2. Answer the questions below in essay format. Your essay must include an introduction,

a body, and a conclusion. It must address all relevant parts of each question. Your

response should be a minimum of 500 words in length, and it should include your

analysis of the probability calculations. Make sure to cite any source you use. Proper

citation format for a source includes the name of the author(s), the title of the work,

the date of the publication, and the page number if you directly quote the source.

Essay: Probability

Using the Quality Summary and Call Center Data, provide a summary report for the vice

president including the following information in an essay with a minimum of 500 words:

1. Based on the probability of an error provided in the quality summary under call quality

using a sample size of 15, predict the probability of both < 2 errors or errors using the
correct discrete probability distribution. Assume calls are either correct or incorrect.
2. Using the call time mean and standard deviation from the quality sample, find the
probability of a call time < 7min, between 7 and 9 min, and > 9 min.

3. Calculate and evaluate the 95% confidence interval for the mean from the call time

data.

Answer

The central limit theorem and the typicality of the disseminations are basic components

for insights and utilized for the rest of the lessons. “The Central Limit Theorem

expresses that the example methods for huge estimated tests will be ordinarily

disseminated paying little heed to the state of their populace appropriations” (Donnelly,

2015, p. 301). For this situation, we have to know the room for mistakes and the

standard blunder are two unique ideas. The room for give and take, or the width of the

interim, is the basic z-score duplicated by the standard mistake for the mean. Be that as

it may, a bigger example lessens the standard mistake and, along these lines, the room

for give and take.

Typical conveyances utilize the z-score estimation, which you found out about in Lesson

2, to recognize the likelihood. To additionally develop this idea, there are times when

you should discover the probabilities that are > < or some place in the middle of two
distinctive z-scores (Donnelly, 2015). In light of the likelihood of a blunder gave in the
quality synopsis under call quality utilizing an example size of 15, we have n = 15 calls.
The consequent phase is to determine the likelihood of <2 blunders. P (mistake) = 0.15.
At that point we make utilization of binomial likelihood recipe: (x < = 2) = P(x=0) +
P(x=1) + P(x=2); P(x=0) = 15C0 * 0.15^0 * 0.85^15 = 0.08735; P(x=1) = 15C1 * 0.15^1
* 0.85^14 = 0.23123; P(x=2) = 15C2 * 0.15^2 * 0.85^13 = 0.28564. In this manner, we
have P(X<=2) = 0.28564 + 0.23123 + 0.08735. The last answer will be P(x < = 2) =
0.604225. The calls are perfect.
Binomial Probabilities
Data
Sample size
Probability of an event of interest
15
0.15
Statistics
Mean
Variance
Standard deviation
2.25
1.9125
1.3829
Binomial Probabilities Table
X
P(X)
0.0874
0.2312
0.2856
0.2184
0.1156
0.0449
0
1
2
3
4
5
<2
0.3186
>=5

0.0617

6

7

8

9

10

11

12

13

14

15

0.0132

0.0030

0.0005

0.0001

0.0000

0.0000

0.0000

0.0000

0.0000

0.0000

We have the quantities of test size, mean and standard deviation figured through

exceed expectations. The example estimate is 15, Mean is 12.05, Standard Deviation is

4.502. The second inquiry is to discover P(X<7). Since (x-mean)/standard deviation=2,
P(2<(7-12.05)/4.502)=P(z<-1.12)=P(z>1.12)=1-P(z>1.12). With a z appropriation

table, the last answer will be P(x<7) =1-0.869=0.131. The subsequent stage is to
ascertain the likelihood in the vicinity of 7 and 9. P(70.68)- 0.131=1-P(z<0.68)- 0.131=0.1169. P(x>9)

=P (z> (9-12.05)/4.502) =P (z>-0.68) =P (z<0.68) =0.752.
When computing the certainty interim populace standard deviation is known, we utilize
the z conveyance, with the recipe of mean +-Za /2* standard blunder. Standard mistake
is a critical piece of utilizing the central limit theorem. Standard mistake is unique in
relation to examining blunder. This measurement centers on the standard deviation
versus the mean. We require standard mistake to discover the certainty interim.
Standard error= standard deviation/sqrt test size=4.502/sqrt15= 1.16. The estimation
of 1.96 depends on the way that 95% of the territory of a typical circulation is inside 1.96
standard deviations of the mean; 1.16 is the standard blunder of the mean. LCL=12.05 (1.96) (1.16) = 9.776, UCL=12.05 + (1.96) (1.16) = 14.32.
All in all, the likelihood of either < 2 mistakes or = 5 blunders is 0.604. The likelihood of
a call time < 7 min is 0.131, the likelihood of a call time in the vicinity of 7 and 9 min is
0.1169, and the likelihood of a call time > 9 min is 0.752. Moreover, we should know

about the meaning of the certainty interim for the mean – an interim gauge around the

example imply that gives a range of where the genuine populace means

falsehoods.

Calculate and evaluate the 95% confidence interval for the mean from the call

time data.

o

Problem uses t critical value since you do not know population standard

deviation and you are using the sample standard deviation.

11.07 +/- (1.98)(3.38/sqrt(150)= 10.52, 11.61

Reference:

Donnelly, R. A. (2015). Business statistics (2nd ed.). Upper Saddle River, NJ:

Pearson.

…

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