STATISTICS TEST # 2 SOLUTIONS |
This is a 2-hour test.
Numbers in parentheses ( ) are mark values.
Answers are in brackets [ ]
In each question list the information given and show your work:
1/ Convert each of the following probabilities to odds:
a) The probability is 4/50.[ odds are 46 : 4 or 23 : 2 against a win ]
b) the probability is 4/75 [ odds are 71 : 4 against being chosen ](4)
2/ Convert each of the following odds to probabilities:
a) The odds are 15 to 3 [ probability is 15/18 or 5/6 = 0.833 ]
b) The odds are 99 to 1 [ probability is 1/100 = 0.01 ] (4)
3/ 2 conditions for a function to serve as a probability distribution are:
a) [ 0 [ f(x) [ 1 ] and b) S f(x) = 1 ] (2)
4/ Which of the following can be a probability distribution? Justify your answer.
a) [ yes ] both conditions are satisfied.
f(0) = 0 | f(1) = 1/10 = 0.1 | f(2) = 2/10 = 0.2 | f(3) = 3/10 = 0.3 | f(4) = 4/10 = 0.4 |
b) [ no since S f(x) = 0.85 ]
c) [ no since f(0), f(1), f(2) are negative ] (6)
5/ (a) Find the mean of this probability distribution. [ l = S (x P(x)) = 1.7 ]
(b) variance:[ r 2 = 2.31 ] standard deviation: [ r = 1.52 ] (5)
6/a) [ µ = 32; r = 4 ] (2)
b) k = 2, so Chebyshev says [ probability is at least 75% that x is between 24 and 40 ] (3)
7/ a) P(x > 2) = 1 - [ P(0) + P(1) + P(2) ] = 0.987
b) [ P(x = 6) = 0.251 ]
c) [ P(x < 2) = 0.013 ] (6)
8/
a) exactly 2 [ 0.116 ] | b) exactly 3 [ 0.170 ] | c) at most 3 [ 0.351 ] |
Note: e - 4.4 = 0.012 (6)
9/ a) exactly 18 [ 0.0723 ]
b) at least 18 [ 0.7673 ]
c) at most 16 [ 0.1685 ] (6)
MAKE A DIAGRAM FOR EACH PART OF THE NEXT 2 QUESTIONS!!
10/ Find the standard-normal curve area which lies:
a)
b)
c)
(3)
11/ Find z if the standard-normal-curve area
a)
b)
c)
(3)
TOTAL (50)
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