Level 2, Suite 5B & 6A, 1-17 Elsie Street, Burwood, NSW 2134
STA101 Business Statistics – Portfolios
Semester 1 2020
Cover Sheet – Portfolios
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Name | Number | |
| Student | |
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| Unit | STA101 Business Statistics | |
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| Lecturer/Tutor | |
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| Assignment title | Assignment 1 (Part 2) | ||
| Marks | 50 Effective: 10% | ||
| Length | Max 5 pages(excluding cover page and references) | Due date | 9th May 2020,before 11pm |
Turnitin Submission(word processed or pdf file)
Declaration
☐ We hereby certify that no part of this assignment has been copied from any other student’s work or from any other source except where due acknowledgement is made in the assignment.
☐ We hereby certify that no part of this assignment has been submitted in another assessment.
☐ No part of the assignment has been written for us or produced for us by any other person.
☐ We am aware that this work will be reproduced and submitted to text matching software for the purpose of detecting possible plagiarism.
Signature of the student:______________________________
This assignment will not be marked if the above declaration is not signed
Question 1 4 Marks
- You have been asked by the sales and marketing department to obtain some initial customer feedback on six new mobile phone models that your company is considering selling. The plan is to successively show each phone to a sample of customers for 30 seconds to gauge their initial reaction to the new models. You are concerned that the order in which customers view the new phone models may influence their feedback (i.e., 1st, 2nd, 3rd, 4th, 5th or 6th).
- If we want each participating customer to view a different arrangement of the six phone models, how many customers will be needed in our sample? (Hint: how many different ways can these phones be arranged for customer viewing?) (2 Marks)
- Rather than showing all six phone models to each participating customer, you have decided to show only three models. If we want to ensure each possible arrangement is viewed by at least one customer, how many customers will be in our sample? (2 Marks)
Question 2 6 Marks
Television commercials are designed to appeal to the most likely viewing audience of the sponsored program. However, Ward (2016) notices that children often have a very low understanding of commercials, even those designed to appeal especially to children. The accompanying table gives figures from Ward’s studies, the percentages of children who do or do not understand TV commercials, for the age groups listed. Suppose now that an advertising agent has shown a television commercial to a six-year-old child and then to a nine-year-old child in a laboratory experiment to test their understanding of the commercials.
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Age | |
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5-7 | 8-10 | 11-12 |
| Do not understand (%) | |
55 | 40 | 15 |
| Understand (%) | |
45 | 60 | 85 |
- What is the probability that the six-year-old child understands the commercial? (2 Mark)
- What is the probability that both children demonstrate an understanding of the TV commercials? (2 Marks)
- What is the probability that one or the other or both children demonstrate an understanding of the TV commercials? (2 Marks)
Question 3 4 Marks
The manager of a large computer network has developed the following probability distribution of the number of interruptions per day:
| Interruptions (X) | P(X) |
| 0 | 0.32 |
| 1 | 0.35 |
| 2 | 0.18 |
| 3 | 0.08 |
| 4 | 0.04 |
| 5 | 0.02 |
| 6 | 0.01 |
- Calculate the mean or expected number of interruptions per day. (2 Mark)
- Calculate the standard deviation. (2 Marks)
Question 44 Marks
If X is a normal random variable with a mean of 78 and a standard deviation of 5, find the following probabilities:
- P(X ≥ 78) (1 Mark)
- P(X ≥ 87) (1 Mark)
- P(X ≤ 91) (1 Mark)
- P(70 ≤ X ≤ 77) (1 Mark)
Question 5 4 Marks
Historical data collected at the Commonwealth Bank in Sydney revealed that 60% of all customers applying for a certain type of loan are accepted. Suppose that 15 new loan applications are selected at random.
- What is the probability that at least 12 loans will be accepted? (1 Mark)
- What is the probability that exactly 10 loans will be accepted? (1 Mark)
- What is the probability that the number of loans rejected is between 8 and 12, inclusive? (1 Mark)
- What is the mean and the standard deviation of number of loans accepted? (1 Mark)
(Hint: Binomial probabilities)
Question 6 4 Marks
It is often important to monitor traffic on a website as organisations need to obtain information about online interactions with their clients. For example, businesses applying for an Australian Business Number (ABN) are asked at the end of the process how long it has taken. Assume that ABN online-application times are normally distributed with a mean time of 40 minutes and a standard deviation of 5 minutes. If a random sample of 50 applications is taken,
- What is the probability that the sample mean is less than 38 minutes? (1 Mark)
- What is the probability that the sample mean is between 39 and 41 minutes? (1 Mark)
- The probability is 80% that the sample mean is between what two values symmetrically distributed around the population mean? (1 Mark)
- The probability is 90% that the sample mean is less than what value? (1 Mark)
Question 7 4 Marks
A consumer group wants to estimate the mean electric bill for the month of July for single family homes in a large city. Based on studies conducted in other cities, the standard deviation is assumed to be $60. The group wants to estimate the mean bill within ± $15 with 99% confidence.
- What sample size is needed? (2 Marks)
- If 95% confidence is desired, what sample size is needed? (2 Marks)
Question 8 10 Marks
The amount of time required to complete a critical part of a production process on an assembly line is normally distributed. The mean is believed to be 130 seconds. To test if this belief is correct, a sample of 100 randomly selected assemblies is drawn and the processing time recorded. The sample mean is 126.8 seconds. If the process time is really normal, with a standard deviation of 15 seconds, can we conclude that the belief regarding the mean is incorrect?
Question 9 10 Marks
In order to determine the number of workers required to meet demand, the productivity of newly-hired trainees is studied. It is believed that trainees can process and distribute more than 450 packages per hour within one week of hiring. Can we conclude that this belief is correct, based on productivity observation of 50 trainees which was found to have an average of 460.38 and standard deviation 38.83?
Question 10 10 Marks
What is the Normal Distribution? What are the characteristics of Normal Distribution?
—-The End—-
Summary Sheet
| Q. | Final Answer/page ref | Marks | Marks |
| Q1(a) | |
2 2 | /4 |
| (b) | |
||
| Q2(a) | |
2 | /6 |
| (b) | |
2 | |
| (c) | |
2 | |
| Q3(a) | |
2 | /4 |
| (b) | |
2 | |
| Q4(a) | |
1 | /4 |
| (b) | |
1 | |
| © | |
1 | |
| (d) | |
1 | |
| Q5(a) | |
1 | /4 |
| (b) | |
1 | |
| (c) | |
1 | |
| (d) | |
1 | |
| Q6(a) | |
1 | /4 |
| (b) | |
1 | |
| © | |
1 | |
| (d) | |
1 | |
| Q7(a) | |
2 | /4 |
| (b) | |
2 | |
| Q8 | |
10 parts | /10 |
| Q9 | |
10 parts | /10 |
| Q10 | |
2 parts | /10 |
Total Marks: /50 Effective /10
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STA101 Business Statistics – Portfolios
