SCM378 Assignment #6 1. A market research study is being conducted to determine if a product modification will be received well by the public. A total of 1,000 consumers are questioned regarding this product. The table below provides information regarding this sample. Positive Reaction Neutral Reaction Negative Reaction Male 240 60 100 Female 260 220 120 a) What is the probability that a randomly selected consumer is a male and has a negative reaction to this change? b) What is the probability that a randomly selected consumer is either a male or has a positive reaction to this change or both? c) If it is known that a consumer has a negative reaction to this change, what is the probability that the consumer is a female? d) A market analyst argues that female customers tend to react to this modification negatively. Prove or disprove this argument statistically using the concept of "statistical independence". 2. Battery manufacturers compete on the basis of the amount of time their products last in cameras and toys. A manufacturer of batteries has observed that its batteries last for an average of 26 hours when used in a toy racing car. The amount of time is normally distributed with a standard deviation of 2.5 hours. a) What is the probability that the battery lasts less than 28 hours? b) What is the probability that the battery lasts longer than 27 hours? c) What is the probability that the battery lasts less than 25 hours? d) What is the probability that the battery lasts between 24 and 28 hours