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(ISOM111)[2006](f)midterm~ac_lfyab^_10366.pdf
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ISMT111 Business Statistics
Midterm Examination
For sections 3 & 4 only
23rd October 2006

Directions
1) Answer ALL FIVE questions. Marks are shown in square brackets.
2) There are 4 pages in this examination paper, which includes a normal table. Check to make sure you have a complete set and notify the invigilator immediately if part of it is missing.
3) Key formulas are provided separately.
4) Calculator may be used in this examination.
5) You are given TWO HOURS to complete this examination. Do not begin until you are told to do so.
Question 1: [15 Marks]
Question 2: [18 Marks]
(a) Why probability can explain the variation in data sets?
The following table gives the first week and annual performance of the stock market index S&P 500 from 1950 to 2003. In 34 of the 54 years from 1950 to 2003, the S&P 500 finished higher after the first 5 days of trading (first week). In 29 of those 34 years S&P 500 finished higher for the year. Answer the following questions to see if a good first week is a good forecast for the upcoming year.
S&P 500 annual performance
First week Higher Lower
Higher 29 5
Lower 10 10

(b)
Given that the S&P 500 finished higher after the first five days of trading, what is the conditional probability that it finished higher for the year?

(c)
Are the two events first week performance and annual performance independent?

(d)
A financial analyst proposed another method to forecast the annual performance of S&P 500. The method, when applying to the data from 1950 to 2003, gives correct forecasts 28 of 39 years S&P 500 ended up higher, while for those years S&P 500 ended up lower the method is correct 13 of 15 years. For 2007, the method forecasts that the S&P 500 will end up higher, what is the probability that the forecast is correct?



Question 3: [20 Marks]
Suppose the skill level X of students in a large statistics course is normally distributed. A student can answer a question correctly in an examination if he (or she) has skill level higher than that required by the question.
(a)
Suppose X has mean 1.2 and standard deviation (s.d.) 0.3. For a question which requires a skill level of 1.6, what is the proportion of students answer it correctly?

(b)
What is the range of skill levels for the middle 50% of students?

(c)
Suppose we do not know the mean and s.d. of skill levels but know that 33% of students answer correctly a question which requires a skill level of 1.8 and 67% of students answer correctly a question which requires a skill level of 1.2. Please find the mean and s.d. of skill levels for students.

(d)
If we only know that the distribution of X is symmetric and it is know that 50% of the students answer correctly a question which requires skill level 1.6 and 25% of the students answer correctly a question of skill level 2.3. Please find the inter-quartile range of X.



Question 4: