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1
. A statistics professor has just given a final e
x
amination in his statistical inference course.
He is particularly interested in learning how his class of
4
0
students performed on this exam. The scores are shown below.
77
8
1 74 77 79 7
3
80 8
5
8
6
73
83 84 81 73 75 91 76 77 95 76
90 85 9
2
84 81 64 75 90 78 78
82
78 86 86 82 70 76 78 72 93
What is the mean score on this exam?
2. In February 2002 the Argentine peso lost 70% of its value compared to the United States dollar. This devaluation drastically raised the price of imported products. According to a survey conducted by AC Nielsen in April 2002, 68% of the consumers in Argentina were buying fewer products than before the devaluation,
24
% were buying the same number of products, and 8% were buying more products. Furthermore, in a trend toward purchasing less-expensive brands, 88% indicated that they had changed the brands they purchased. Suppose the following complete set of results were reported. Use the following data to answer this question.
|
Number of Products Purchased |
||||||
|
Brands Purchased |
Fewer |
Same |
More |
Total |
||
|
10 |
14 |
24 |
48 |
|||
|
Changed |
262 |
82 | 8 |
352 |
||
|
272 |
96 |
32 |
400 |
What is the probability that a consumer selected at random purchased fewer products than before?
3.The following data were obtained from a survey of college students. The variable X represents the number of non-assigned books read during the past six months.
| x | 0 | 1 | 2 | 3 | 4 | 5 | 6 |
|
P (X=x) |
0.55 |
0.15 |
0.10 |
0.04 |
0.03 |
Find P(1 < X < 5).
4. An ice cream vendor sells three flavors: chocolate, strawberry, and vanilla. Forty five percent of the sales are chocolate, while 30% are strawberry, with the rest vanilla flavored. Sales are by the cone or the cup. The percentages of cones sales for chocolate, strawberry, and vanilla, are 75%, 60%, and 40%, respectively. For a randomly selected sale, define the following events:
= chocolate chosen
= strawberry chosen
= vanilla chosen
= ice cream on a cone
ice cream in a cup
Find the probability that the ice cream was vanilla flavor, given that it was sold in a cup.
5. If Z is a standard normal random variable, then the value z for which P(-z < Z < z) equals 0.8764 is
