Statistics and probability question.

Franklin University
Math 280 – Introduction to Probability and Statistics
Name: __________________________
Module 5 Application Assignment (16 Points)
NETWORK SPEEDS AND CUSTOMER RELIABILITY
You are a network manager for a large, regional Internet Service Provider (ISP) and telecommunications
company. Your company markets and sells two levels of network access: a residential service which
includes a 50 Mbps download / 20 Mbps upload Internet connection, and a business service package
which includes a 100 Mbps download / 60 Mbps upload Internet connection. Your Regional Vice
President has asked for your help with some analysis of the network in connection with an annual
review of your company’s marketing and advertising claims. You asked your best network administrator
to provide you with the mean and standard deviation of the download and upload speeds for both your
resident and business class Internet services. They have confirmed that your network speeds are all
approximately normally distributed and provided the following data based on a complete census of your
customer data:
Performance
Metric
Mean (𝜇)
Standard
Deviation (𝜎)
Residential Service
(50 Mbps download / 20 Mbps upload)
Download
Upload
56.7
21.7
2.3
0.8
Business Class Internet Service
(100 Mbps download / 60 Mbps upload)
Download
Upload
105.0
61.5
3.2
1.7
1. (8 pts) Create a series of shaded normal distribution plots showing (and calculating) the following:
a. The proportion of residential customers whose download speed are less than 50 Mbps.
b. The proportion of residential customers whose upload speeds are greater than 20 Mbps.
c. The proportion of residential customers whose download speeds are between 54 and 61 Mpbs.
d. The proportion of business customers whose download speeds are greater than 100 Mbps.
e. The proportion of business customers whose upload speeds are less than 60 Mbps.
f.
The proportion of business customers whose upload speeds are between 57 and 63 Mpbs.
g. Which of these four services has the lowest reliability? What percentage of customers using this
service receive the download or upload speeds advertised?
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081020
Franklin University
Math 280 – Introduction to Probability and Statistics
Name: __________________________
2. (8 pts) Answer the following questions about one area of town that is particularly prone to
competition for Internet services where your company has 125 residential Internet customers and
87 business customers.
a. What is the probability that any single residential customer would experience download speeds
below 57 Mbps? (Include a shaded probability plot with your answer.)
b. What type of distribution would be used to describe the average value of download speeds of
all 125 residential customers in this area? Using correct mathematical symbols, what would the
mean and standard deviation of this new distribution be? (No graph needed.)
c. What is the probability that the average download speed of all 125 residential customers in this
area is less than 57 Mbps? (Include a shaded probability plot with your answer.)
d. If this area had 200 residential customers instead of 125, would the probability you found in part
c) increase or decrease? Justify your answer.
e. What is the probability that any single business customer would experience download speeds
above 106 Mbps? (Include a shaded probability plot with your answer.)
f.
What type of distribution would be used to describe the average value of download speeds of
all 87 business customers in this area? Using correct mathematical symbols, what would the
mean and standard deviation of this new distribution be? (No graph needed.)
g. What is the probability that the average download speed of all 87 business customers in this
area is more than 106 Mbps? (Include a shaded probability plot with your answer.)
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