A new type of smoke detector battery is developed. From laboratory rests under standard co...

A new type of smoke detector battery is developed. From laboratory rests under standard conditions, the half-life (defined as less than 50 percent of full charge) of 20 batteries are shown below. (a) Make a histogram of the data and/or a probability plot. Do you think that battery half-life can be assumed normal? (b) The engineers say that the mean battery half-life will be 8,760 hours with a standard deviation of 200 hours. Using these parameters (not the sample), set up the centreline and control limits for the  chart for a subgroup size of n= 5 batteries to be sampled in future production runs. (e) Repeat the previous exercise. But this time, use the sample mean and standard deviation. (d) Do you think that the control limits from this sample would be reliable? Explain, and suggest alternatives.