Question 633201: Answer each of the following questions as concisely as possible. Show all necessary working (including graphs, if necessary) and steps to obtain maximum marks.
Scan your answer sheet as a single document and submit electronically.
Question 1: Introduction to Probability Distributions
The following probability distributions of job satisfaction scores for a sample of information systems (IS) senior executives and IS middle managers range from a low of 1 (very dissatisfied) to a high of 5 (very satisfied).
What is the expected value of the job satisfaction score for senior executives?
[7 marks]
What is the expected value of the job satisfaction score for middle managers?
[7 marks]
Compute the variance of job satisfaction scores for executives and middle managers.
[7 marks]
Compute the standard deviation of job satisfaction scores for both probability
distributions.
[7 marks]
Compare the overall job satisfaction of senior executives and middle managers.
[7 marks]
Question 2: Binomial Probability Distribution
A Harris Interactive survey for InterContinental Hotels & Resorts asked respondents,
“When ravellers internationally, do you generally venture out on your own to experience culture, or stick with your tour group and itineraries?” The survey found that 23% of the respondents stick with their tour group (USA Today, January 21, 2004).
In a sample of six international ravellers, what is the probability that two will stick with their tour group?
In a sample of six international ravellers, what is the probability that at least two will stick with their tour group?
[7 marks]
In a sample of 10 international travelers, what is the probability that none will stick with their tour group?
[7 marks]
Question 3: The Normal Distribution
Assume that the test scores from a college admissions test are normally distributed, with a mean of 450 and a standard deviation of 100.
(a) What percentage of the people taking the test score between 400 and 500?
[7 marks]
(b) Suppose someone receives a score of 630. What percentage of the people taking the test score better? What percentage score worse?
[7 marks]
(c) If a particular university will not admit anyone scoring below 480, what percentage of the persons taking the test would be acceptable to the university?
[7 marks]
Question 4: Sampling Distribution
BusinessWeek surveyed MBA alumni 10 years after graduation (BusinessWeek, September 22, 2003). One finding was that alumni spend an average of $115.50 per week eating out socially. You have been asked to conduct a follow-up study by taking a sample of 40 of these MBA alumni. Assume the population standard deviation is $35.
(a) Show the sampling distribution of x ̅, the sample mean weekly expenditure for the
40 MBA alumni.
[7 marks]
(b) What is the probability the sample mean will be within $10 of the population mean?
[8 marks]
(c) Suppose you find a sample mean of $100. What is the probability of finding a sample mean of $100 or less? Would you consider this sample to be an unusually low spending group of alumni? Why or why not?
[8 marks]
Answer by solver91311(24713)   (Show Source):
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