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ISMT111 Business Statistics
Midterm Examination
For sections 1-6 only
14th October 2005

Directions
1) Answer ALL FIVE questions. Marks are shown in square brackets.
2) There are 4 pages in this examination paper. Check to make sure you have a complete set and notify the invigilator immediately if part of it is missing.
3) Key formulas and Statistical tables 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: [22 Marks]
Suppose that there are 100 boxes each containing 5 red balls and 3 black balls. 100 students are assigned to one box each and are asked to pick 4 balls without replacement from his or her box.
(a)
For one box what is the probability that a red ball is chosen on the 2nd and 3rd pick?

(b)
Suppose that Y100 denotes the number of students, out of 100, that will obtain a red ball on the 2nd and 3rd pick. Fnd the mean and variance of Y100.

(c)
Find the probability that no more than 20 students obtain red balls on the 2nd and 3rd pick.

(d)
Suppose that only 10 boxes are considered. Find the probability that no more than 3 students obtain red balls on the 2nd and 3rd pick.

(e)
Suppose that after the first pick from the box, an extra ball of the same color is added to the box with probability .. Otherwise no new ball is added. Given that there is no other change; for the 100 boxes, find the expected number of times an extra red ball is added to a box.

(f)
Suppose that 5 boxes are combined into one box. A student is then asked to take out 11 balls from the box at random. Find the probability that 7 are red.



Question 2: [18 Marks]
An urn has two coins. These coins each has two faces. The probabilities of landing heads (head faces up) for the two coins are:
Coin 1: lands heads with probability .
(coin has head on one side and tail on the other side)
Coin 2: lands heads with probability 1
(coin has heads on both sides)

You select a coin at random (each coin has probability 1/2 of being selected). Then you toss the selected coin,
(a)
What is the probability that the tossed coin lands head?

(b)
What is the probability that you select coin 1 and it lands head?

(c)
Suppose that the tossed coin lands head. Given that information, what is the conditional probability that you selected coin 1? What is the conditional probability that you selected coin 2?

(d)
Given that the tossed coin lands head, what is the conditional probability that the reverse side of this coin (or the side facing down) is tail?



Question 3: [20 Marks]
The time needed to complete the midterm exam for ISMT111 is normally distributed with a mean of 100 minutes and a standard deviation of 15 minutes. 1000 students take the 2-hour exam from 7pm to 9pm. Answer the following questions.
(a)
W