Question 1: According to the latest census, 40% of working women held full time jo.
In a sample 10 working women,
(a) What is the expected number of working women held full time jobs?
(b) What is the probability that none of them held full time job?
(c) What is the probability of more than half of them are not working or working part time?
(d) What assumptions do you need to make to find the probability?
In a sample of 100 working women,
(e) What is the probability that more than half of them held full time job? [Hint: use normal approximate and continuity correction]
Question 2: The Australian Bureau of Statistics (ABS) has collected data on the part-time employment patterns of full-time students in Australia and has found the hours worked to be well approximated by a normal distribution with a mean of 15 hours.
(a) If 10% of students work more than 25 hours per week, what is the standard deviation of the number of hours worked by students?
(b) What is the probability that a student chosen at random works between 5 and 25 hours per week?
(c) What is the number of hours worked per week in order to be in the top 20 percentile?
(d) Suppose that student asks all the members of his/her tutorial group how many hours they work and that there are 36 students in the group. What is the probability that the average number of hours worked is between 5 and 25? State clearly any assumptions you make.
(e) Explain whether it is necessary to assume that the distribution of hours worked is normal when calculating part (d)? If the population standard deviation as determined in (a) is not known, what would be the best estimate.
Question 3: The auditor needs to provide a confidence interval for the mean outstanding balance for a company's clients. From past experience, the distribution of outstanding balances is known to have a variance of 25. Assuming the population distribution of outstanding balances is normal,
(a) Find the 95% confidence interval for the mean outstanding balance if the auditor's sample of 65 accounts produced a sample mean of $140? Do you need to assume normality for the population distribution to answer the question? Explain.
(b) Suppose that before the survey is undertaken, the auditor wants to ensure that the 95% confidence interval for the mean outstanding balance that ends up with a total width of no more than 0.5. How many people should the auditor has sought to survey?