__Problem 1 __

As a result of government and consumer pressure, automobile manufacturers in the Unites States are deeply involved in research to improve their products’ gasoline mileage. One manufacturer, hoping to achieve 40 miles per gallon on one of its compact models, measured the mileage obtained by 36 test versions of the model:

43 35 41 42 42 38 40 41 41 40 40 41 42 36 43 40 38 40

38 45 39 41 42 37 40 40 44 39 40 37 39 41 39 41 37 40

a) Find the mean and standard deviation of these data and give the units in which they are expressed.

b) If the manufacturer would be satisfied with a (population) mean of 40 mpg, how would they react to these test data?

c) Use the information in Tables 2.6-2.7 in the text book to check the reasonableness of the calculated standard deviation s=2.2 (i.e., use the Chebyshev rule and the Empirical rule to estimate the standard deviation based on the range of the data. Does the answer of s=2.2 look reasonable, based on these two calculations?)

d) Construct a relative frequency histogram of the data set. Is the data set mound-shaped?

e) What percentage of the measurements would you expect to find within the mean+/-1s, mean+/-2s, mean+/-3s?

f) Count the number of measurements that actually fall within the intervals of part e. Express each interval count as a percentage of the total number of measurements. Compare (interpret) these results with respect to your answers in part e.

__Problem 2 __

The U.S. Census Bureau reports that the percentage of mothers with infant children in the workforce has declined since 1998. The following table gives a breakdown of the marital status and working status of the 3.9 million mothers with infant children in the year 2000. (The numbers in the table are reported in millions.) Consider the following events: A = {Mom with infant works}, B = {Mom with infant is married and living with husband}. Are A and B independent events? Justify your answer.

Working | Not Working | |

Married/living with husband | 1385 | 1175 |

All other arrangements | 786 | 588 |

__Problem 3 __

The following table lists the number of carloads of different types of commodities that were shipped by the major U.S. railroads during a week. Suppose the computer record for a carload shipped during the week is randomly selected from a master file of all carloads shipped that week and the commodity type shipped is identified.

Type of Commodity |
Number of Carloads |

Agricultural products | 41,690 |

Chemicals | 38,331 |

Coal | 38,331 |

Forest products | 21,929 |

Metallic ores and minerals | 34,521 |

Motor vehicles and equipment | 22,906 |

Nonmetallic minerals and products | 37,416 |

Other carloads | 14,382 |

Total | 335,770 |

a) List or describe the sample points in this experiment.

b) Find the probability of each sample point.

c) What is the probability that the rail car was transporting automobiles? Nonagricultural products?

d) What is the probability that the rail car contained chemicals or coal?

e) One of the carloads shipped that week was in a boxcar with serial number 1003642. What is the probability that that particular carload would be the one randomly selected from the computer file? Justify your answer.

__Problem 4 __

The local area network (LAN) for the college of Business computing system at a large university is temporarily shut down for repairs. Previous shutdowns have been due to hardware failure, software failure, or power failure. Maintenance engineers have determined that the probabilities for hardware, software, and power failure are 0.01, 0.05, and 0.02, respectively. They have also determined that if the system experiences hardware problems, it shuts down 73% of the time. Similarly, if software problems occur, the system shuts down 12% of the time; and, if power failure occurs, the system shuts down 88% of the time.

a) What is the probability that the current shutdown of the LAN is due to hardware failure?

b) What is the probability that the current shutdown of the LAN is due to software failure?

c) What is the probability that the current shutdown of the LAN is due to power failure?

d) If the cost of the expected repairs for hardware, software, and power failure are $45,000, $15,000, and $25,000, what is the expected cost of the current repair?

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