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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