Two companies make batteries for cell phone manufacturers. One company claims a mean life span of 2.5 years, while the other co
mpany claims a mean life span of 3 years (assuming average use of minutes/month for the cell phone). a) Explain why you would also like to know the standard deviations of the battery life spans before deciding which brand to buy. b) Suppose those standard deviations are 1.5 months for the first company and 9 months for the second company. Does this change your opinion of the batteries? Explain.
By definition of mean life we know that on an average the respective phones will last for 2.5 years or 3 years respectively but for each model there will be phones which last less than the mean life and phones which last for greater than the mean life.A lower standard deviation means that all the phone batteries have life close to mean life while as a larger standard deviation means that the lives of the batteries are spread out. The Percentage of such phone which last for time greater or lesser than mean depends on the standard deviation of the data.
Since we will get a phone at random from the samples we need to maximize our chances of getting a better phone which can be obtained only if we know the standard deviation of the data.
Part b)
Yes it changes our opinion of the given batteries since for the battery with life of 2.5 years has a lesser deviation thus we infer if we choose any battery from this sample at random we have larger chances that the battery has the specified or greater life span while as the chances in the second type of battery are lower.
