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1)
Find 999+997+995+993+...+161.
2)
Is the folowing number perfect, deficient or abundant?
a)
1995;
b)
1997;
c)
1999.

3)
Find 610+611+612+...+629.

4)
An experiment consists of rolling 2 dice. Consider the 2 events:
A = sum of the numbers on the 2 dice is 5;
B = at least one of the dice shows a number that is divisible by 3;
C = at most one of the dice shows an even number.
Find P(A),P(B), $P(A \cap B)$, P(A|B),$P(A\cap C)$, P(A|C),P(B|C);

5-6)
Each day, there is a 3/5 probability that the price of a certain stock rises one point, and a 2/5 probability that the price drops one point.
a)
Find the probability that the stock rises exactly 5 days during 8 days.
b)
Find the probability that the stock rises at least 6 days during 9 days.
c)
Suppose that the stock price has risen by a total of exactly 40 points after 90 days. How many days that the stock rises on and how many days that the stock fall on?
d)
Find the probability that the stock price has risen by a total of exactly 4 points after 10 days.
e)
Find the probability that the stock price has risen by a total of at least 2 points but at most 6 points after 10 days.

7)
Eighteen runners race around a track.
a)
Assume that there are no ties. How many different orders can they finish in?

b)
The first three runners get medals. How many different groups of medalists can there be?

8)
Given a data set: 13,10,2,-5,7,10,-2
a)
Find the mean, the average derivation and the standard derivation;
b)
Write a five-number summary and draw a boxplot.

9)
Is the given point inside, outside or on the hypersphere of radius 8 centered at (-3,6,8,6)?
a)
(-1,2,5,0);
b)
(1,9,9,7);
c)
(1,9,9,8).

10)
Find the equation of the hypersphere centered at (1,9,9,8) that passes through (2,0,5,0).

11)
Let P be on the sphere centered at (2,-2,2) that passes through (0,0,0) and let Q be on the sphere centered at (-6,-4,6) that passes through (-5,-5,5). Find the maximum and minimum value of the distance between P and Q.


 
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Jie Wu
11/21/1997