1. In a poll, respondents were asked whether they had ever been in a car accident. 177 respondents indicated that they had been in a car accident and 107 respondents said that they had not been in a car accident. If one of these respondents is randomly selected, what is the probability of getting someone who has been in a car accident?
2. The data set represents the income levels of the members of a country club. Find the probability that a randomly selected member earns at least $102,000

   INCOME (Thousands of dollars)

   108   128     82   138    85   108    88    76   158   208

   79     98   148    85   128   118    88   168    73   118

3. In a certain class of students, there are 13 boys from Wilmette, 3 girls from Kenilworth, 11 girls from Wilmette, 6 boys from Glencoe, 5 boys from Kenilworth and 6 girls from Glencoe. If the teacher calls upon a student to answer a question, what is the probability that the student will be from Kenilworth?
4. Find the probability of correctly answering the first 2 questions on a multiple choice test if random guesses are made and each question has 4 possible answers.
5. Of 1906 people who came into a blood bank to give blood, 300 people had high blood pressure. Estimate the probability that the next person who comes in to give blood will have high blood pressure.

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1. A smart meter updates the status of the electricity usage every 12 hours to the central controller. It sends out an indictor message wirelessly and the message is received at the controller with probability p. If the message is received successfully, then the controller sends a ACK message to the smart meter. For errored reception, NAK message is sent. The ACK/NAK message is received with probability q. It is known that p = 0:9 and q = 1 for this communication network scenario. If NAK message is received then the smart meter sends the same indicator message again, and the maximum number of times such repeated message sending is allowed is K. Assume independent message transmission. If correct message is not received after K attempts (including the original one), the controller alerts the network operator to take action. (a) If K = 2, what is the probability that the network operator has to act on this meter reading? (b) If the probability of alerting the network operator has to be less than 0.01%, how many attempts should be tried. (c) Discuss the trade-off of communication cost and technician cost. 2. Let X be the input to a communication channel and let Y be the output. The input to the channel is +1 volt or -1 volt with equal probability. The output of the channel is the input plus noise voltage N that is uniformly distributed in the interval -2 volts to +2 volts. Find P[X = +1; Y _ 0]. 3. A communication system accepts a voltage V and outputs a voltage Y = _V + N, where _ = 10?2 and N is Gaussian random variable with parameters m = 0 and _ = 2. Find the voltage value of V that gives P[Y

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PERT & CPM

Widgetco is about to introduce a new product. One unit of this product is produced by assembling subassembly 1 and subassembly 2. Before production begins on either subassembly, raw materials must be purchased and workers must be trained. Before the subassemblies can be assembled into the final product, the finished subassembly 2 must be inspected. A list of activities, their predecessors, and their durations is given in the following Table.

Activity Predecessors Duration(days) A – Train workers ——— 6 B – Purchase raw materials ——— 9 C – Make subassembly 1 A,B 8 D – Make subassembly 2 A,B 7 E – Inspect subassembly 2 D 10 F – Assemble Subassemblies C,E 12
Problem:

1. Draw a project diagram (network) for this project?
2. What is the total project time?
3. What is the critical path?
2. DECISION ANALYSIS

Visual Tech is considering marketing one of two new video games for the coming holiday season: Battle Pacific or Space Pirates. Battle Pacific is a unique game and appears to have no competition. Estimated profits (in thousands of dollars) under high, medium, and low demand as follows:

Demand Battle Pacific High Medium Low Profit $1000 $700 $300 Probability .2 .5 .3 Visual Tech is optimistic about its Space Pirates game. However, the concern is that profitability will be affected by competitors’ introduction of a video game viewed as similar to Space Pirates. Estimated profits (in thousands of dollars) with and without competition is as follows:

Demand Space Pirates
With Competition High Medium Low Profit $800 $400 $200 Probability 0.3 0.4 0.3
Demand Space Pirates
Without Competition High Medium Low Profit $1600 $800 $400 Probability 0.5 0.3 0.2

Problem:

Develop a decision for Visual Tech problem?
If Visual Tech believes that its competitor will launch the similar Space Pirates with probability 0.6. The director of planning recommends marketing the Battle Pacific video game. …

BUS 4025 – Assignment 7
For these problems, please use Excel to show your work, and submit the Excel spreadsheet along with your completed assignment.
For the following problems, state the null and alternate hypothesis, find the chi-square test statistic, decide whether to reject or fail to reject the null hypothesis, and provide your analysis and conclusions.
Results from a survey five years ago that asked how long they had to wait in the waiting room to see their doctor. You randomly selected 250 people and asked them how long they had to wait in the waiting room. Can you conclude at sig. of .01 that there has been a change in claimed or expected distribution?
Actual Minutes
Actual Percentage
Survey Result Minutes
Survey Result Frequency
1 – 5
14%
1 – 5
21
6 – 10
18%
6 – 10
39
11 – 15
27%
11 – 15
37
16 – 20
15%
16 – 20
53
21 – 25
11%
21 – 25
40
26 – 30
9%
26 – 30
34
31 and over
6%
31 and over
26
Results from a previous survey asked baseball players on a high school team what they needed help with the most in baseball. To determine whether the distribution is the same, a researcher studied 125 randomly selected players and asked them what they needed the most help with. The results are shown below. At a sig. of .05 are the distributions the same?
Actual Percentage
Survey Result
Bunting
11%
18
Batting Approach
38%
33
Strategy
26%
47
Throwing Velocity
25%
27
For the following problems, find the expected frequencies of each cell in the table, perform a chi-square test for independence, and comment on the relationship between the variables. Assume the variables are independent.
The contingency table shows the results of a random sample of college professors and the years of teaching at the university level.
Gender

Ryerson University CN8814 -Network Mathematics and Simulation -Winter 2013 Select Problems 1. Let X be a random variable that represents the percentage of time a computer processor is active in any day. The cumulative density function (CDF) of X is given by FX(x) = K(x2 + 3x); 0 x 1 where K is a constant. (a) What is the value of K? (b) Determine the probability density function (PDF) of X. (c) Calculate the average percentage of time the processor is idle? (d) Let Y be a random variable that represents the percentage of time an external memory is accessed from the computer in any day. Y is modeled as Y = 2X??1. Determine the average percentage of time the memory is accessed. (e) Calculate the variance of Y . 2. In a iPhone assembling factory, a robot installs a single camera in each phone. The camera is randomly picked from one of the three boxes that have cameras from three different makes. Let these boxes be labeled B1;B2 and B3. Assume that the box selection is fair. The probability that the camera is box B1;B2 and B3 is defective is 0.01, 0.03 and 0.05 respectively. (a) What is the probability that the assembled iPhone has a defective camera in it? (b) Given that the iPhone is defective, what is the probability the camera was from manufacturer B1 (i.e., it is from box B1)? (c) If two cameras are installed in an iPhone, what is the probability that the assembled iPhone has no defective camera? 1
3. A node in a network has access to two data links (namely L1 and L2) to send its packets. It uses link L1 with probability p. Link L1 does not queue the transmitted packets (meaning that it always sends the received packets to the next node immediately); however, L2 queues the packets with probability q (as it serves more than one node). All the packets are sent eventually to the Internet, and then they are received at the end-device and re-assembled according to the protocol. (a) What is the probability that a packet will be delayed (or queued) if p = 0:8 and q =…

1. A smart meter updates the status of the electricity usage every 12 hours to the central controller. It sends out an indictor message wirelessly and the message is received at the controller with probability p. If the message is received successfully, then the controller sends a ACK message to the smart meter. For errored reception, NAK message is sent. The ACK/NAK message is received with probability q. It is known that p = 0:9 and q = 1 for this communication network scenario. If NAK message is received then the smart meter sends the same indicator message again, and the maximum number of times such repeated message sending is allowed is K. Assume independent message transmission. If correct message is not received after K attempts (including the original one), the controller alerts the network operator to take action. (a) If K = 2, what is the probability that the network operator has to act on this meter reading? (b) If the probability of alerting the network operator has to be less than 0.01%, how many attempts should be tried. (c) Discuss the trade-off of communication cost and technician cost. 2. Let X be the input to a communication channel and let Y be the output. The input to the channel is +1 volt or -1 volt with equal probability. The output of the channel is the input plus noise voltage N that is uniformly distributed in the interval -2 volts to +2 volts. Find P[X = +1; Y _ 0]. 3. A communication system accepts a voltage V and outputs a voltage Y = _V + N, where _ = 10?2 and N is Gaussian random variable with parameters m = 0 and _ = 2. Find the voltage value of V that gives P[Y

1-Fast service Truck lines uses the ford super 1310 exclusively. management made a study of the maintenance costs and determined the number of kilometers travelled during the year followed the normal distribution . the main of distribution was 96,000 km and the standared deviation 3200 km/
What percent of the ford super 1310s logged 104 970 km or more?
What percent of the trucks logged more than 91,800 but less than 93 800 km?
What percent of the fords travelled 99 800 or less during the year?
Is it reasonable to conclude that any of the trucks were driven more than 112 700 km? Explain.
2- the average salary of merchandisers’ is$ 45,000 per year with a standard deviation of $6000.
What is the probability that a merchandiser s earns more than $55,000 per year?
What is the probability that a merchandiser s earns less than $32000 per year
What is the probability that a merchandiser s earns between $40,000 and 50,000 per year?
What is the probability that a merchandiser s will earns between $36,000 and $54,000 per year?
What is the average salary blew which 20 percent of the mechandisers earn?
What is the average salary above which the top 10 percent of mechaandisers earn?

For the following problems:
1. State the Null Hypothesis and the Alternative Hypothesis
2. Determine the test statistic.
3. Determine the P-value
4. Make a decision regarding the hypotheses based on the P-value and the Level of
Significance.

3. Do middle-aged male executives have different average blood pressure than the general population? The National Center for Health Statistics reports that the mean systolic pressure for males ages 35 to 44 is 128 and the standard deviation of this population is 15. The medical director of a company looks at the medical records of 72 company executives in this age group and finds that the mean systolic blood pressure in this sample is 126.07. Is this evidence that executive blood pressures differ from the national average? Use a 5% level of significance.
4. In fiscal 1996, the U.S. Agency for International Development provided 238,300 metric tons of corn soy blend (CSB) for development programs and emergency relief in countries throughout the world. CSB is a highly nutritious, low-cost fortified food that is partially cooked and can be incorporated into different food preparations by the recipients. The specifications for the CSB state that the mixture should contain 2 pounds of vitamin premix for every 200 pounds of product. These specifications are designed to produce a mean vitamin C content in the final product of 40mg per 100g. A sample of 8 readings from a production run has a mean of 22.50mg per 100g with a standard deviation of 7.19mg per gram. Is there significant evidence that this production run does not meet the specifications? Use a 1% level of significance.

5. According to the National Institute for Occupational Safety and Health, job stress poses a major threat to the health of workers. A national survey of restaurant employees found that 75% said that job stress had a…

Australia DataLife expectancy at birth, total (years)CO2 emissions (metric tons per capita)GDP growth (annual %)Health expenditure per capita (current US$)19951996199719981999200020012002200320042005200620072008Mobile cellular subscriptions (per 100 people)Year\Indicator Name77.8317.011574.283.9412.3778.0817.981767.724.1821.7878.4818.021766.053.9724.7178.6318.541597.624.5926.2578.9317.201754.985.1633.3379.2317.211728.463.9544.6879.6316.731644.802.0757.4379.9417.371858.493.9064.6380.2417.412339.223.2772.3180.4917.352888.984.1681.9780.8418.013157.752.9690.2881.0418.233330.213.0895.2681.2918.073956.473.56100.6681.4018.574229.033.83102.82

1. The National Student Loan Survey collects data to examine questions related to the amount of money that borrowers owe. The survey selected a sample of 1280 borrowers who began repayment on their loans between 4 and 6 months prior to the survey. The mean debt for undergraduate study was $18,900 and the standard deviation was about $49,000 (This is the correct value!). Construct a 95% confidence interval for the true mean debt for the student borrowers.

2. Twenty-five volunteers who had developed cold symptoms within the last 24 hours were given zinc lozenges to take every 2 to 3 hours until their cold symptoms were gone. The mean overall duration of symptoms was 4.5 days with a standard deviation of 1.6 days. The selected cases have a distribution which appears to be symmetric and bell-shaped.

Construct a 99% confidence interval for the mean overall duration of symptoms in a
population of individuals who used zinc lozenges.

In a previous test, the mean overall duration of symptoms for volunteers who were
told to drink an herbal tea for relief of their symptoms was 7 days. Based on your
confidence interval, do you think that using the lozenges reduces the overall duration
of symptoms compared to using the herbal tea?

For the following problems:
1. State the Null Hypothesis and the Alternative Hypothesis
2. Determine the test statistic.
3. Determine the P-value
4. Make a decision regarding the hypotheses based on the P-value and the Level of
Significance.

3. Do middle-aged male executives have different average blood pressure than the general population? The National Center for Health Statistics reports that the mean systolic pressure for males ages 35 to 44 is 128 and the standard deviation of this population is 15. The medical director of a company looks at the medical records of 72 company executives…

MBA SEMESTER 1 MB0040 – STATISTICS FOR MANAGEMENT-4 Credits (Book ID: B1129) Assignment Set-1 (60 Marks) Note: Each question carries 10 Marks. Answer all the questions 1. (a) ‘Statistics is the backbone of decision-making’. Comment. (b) ‘Statistics is as good as the user’. Comment. 2. Distinguish between the following with example. (a) Inclusive and Exclusive limits. (b) Continuous and discrete data. (C) Qualitative and Quantitative data (d) Class limits and class intervals. 3. In a management class of 100 students’ three languages are offered as an additional subject viz. Hindi, English and Kannada. There are 28 students taking Hindi, 26 taking Hindi and 16 taking English. There are 12 students taking both Hindi and English, 4 taking Hindi and English and 6 that are taking English and Kannada. In addition, we know that 2 students are taking all the three languages. i) If a student is chosen randomly, what is the probability that he/she is not taking any of these three languages? ii) If a student is chosen randomly, what is the probability that he/she is taking exactly one language? 4. List down various measures of central tendency and explain the difference between them? 5. Define population and sampling unit for selecting a random sample in each of the following cases. a) Hundred voters from a constituency b) Twenty stocks of National Stock Exchange c) Fifty account holders of State Bank of India d) Twenty employees of Tata motors.
6. What is a confidence interval, and why it is useful? What is a confidence level? MBA SEMESTER 1 MB0040 – STATISTICS FOR MANAGEMENT-4 Credits (Book ID: B1129) Assignment Set-2 (60 Marks) Note: Each question carries 10 Marks. Answer all the questions 1. What are the characteristics of a good measure of central tendency? (b) What are the uses of averages? 2. Your company has launched a new product .Your company is a reputed company with 50% market share of similar range of products. Your competitors also enter with their new products…