STAT7055 Semester 2 2022 Topic 4 Tutorial Questions
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
STAT7055 Semester 2 2022
Topic 4 Tutorial Questions
1. The amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 30 and 60 minutes. One student is selected at random. Find the probability of the following events:
(a) The student completes the quiz in a time between 30 and 40 minutes.
(b) The student completes the quiz in a time between 30 and 40 minutes, given that
they took less than 45 minutes to complete the quiz.
The professor wants to reward (with bonus marks) students who are in the lowest quarter of completion times.
(c) What completion time should she use for the cutoff for awarding bonus marks?
The professor writes a second quiz which she believes will take students a third as long to complete than the original quiz. Suppose that while the students are taking the second quiz, a blackout lasting 2 minutes occurs, adding 2 minutes to every exam completion time.
(d) Calculate the expected value and variance of the completion time for a student taking the second quiz.
2. For two particular stocks A and B , let RA and RB denote their annual returns, respec- tively. Suppose that RA is uniformly distributed between −12% and 26% and that RB is normally distributed with µ = 15% and σ 2 = 73.96%2 . Further, suppose the probability that both stocks A and B have positive annual returns is 0.67.
(a) In a given year, find the probability that stock A has a negative return, given that
stock B has a positive return.
(b) In a given year, find the probability that both stocks A and B have negative returns.
3. Using the z-tables, find the value of c which makes the following statements true. Note
that:
|Z| = 
(a) P(Z < c) = 0.2
(b) P(|Z| > c) = 0.02
(c) P(|Z| < c) = 0.90
Z < 0
Z ≥ 0
4. A fast food chain pays its teenage employees an average wage of $9.20 per hour with a standard deviation of 50 cents. Assuming wages are approximately normally distributed, answer the following questions:
(a) What proportion of teenage employees receives wages between $8.50 and $10 per
hour?
(b) A new worker insists he will not work unless he is paid the wage earned by the top
0.5% of teenage workers. His sister, also new to the job, takes a different approach and being thankful for the work, has said she will work for the wage that represents the 5th percentile of teenage workers. What is the difference in wages that they are prepared to work for?
5. You are told that investors’ anticipated future returns are normally distributed. You are also told that 4% of investors think they will return above 20% in the coming twelve months, whereas 20% think they will earn less than 8%. What is the mean and standard deviation of the overall distribution of investors’ anticipated future returns?
6. Discussion Question
You have been asked to analyse some data that consists of values recorded for each observation in two samples. You are told that one of the samples was taken from a population that is known to be uniformly distributed and that the other sample was taken from a population that is known to be normally distributed. You are further told that the data will be provided to you in two separate files, one file containing data from one sample and another file containing data from the other sample. If the files were not named or labelled in any way, how could you determine which file, i.e., sample, came from which population? When you eventually receive the data, it turns out the situation was even worse than you thought. Only one file, with no names or labels, was provided that contained all the data for both samples, mixed together. Is there anything you can do now to try and identify the two samples?
7. swirl
Work through lessons 7 and 8 of the R Programming course.
2022-08-31