Probability-Deviation. 1. A statistics professor has just given a final examination in his statistical inference course. He is particularly interested in learning how his class of 40 students performed on this exam. The scores are shown below.

77 81 74 77 79 73 80 85 86 73

83 84 81 73 75 91 76 77 95 76

90 85 92 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 |

Same | 10 | 14 | 24 | 48 |

Changed | 262 | 82 | 8 | 352 |

Total | 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 | 0.10 | 0.04 | 0.03 | 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