A firm produces batteries that have a lifetime which is normally distributed with a mean of 350 minutes and a
standard deviation of 25 minutes. The firm needs to keep an eye on the production process to ensure that everything is working properly and that batteries are not being produced that do not meet the advertised standard. This is done by calculating the mean of the sample. To allow this they regularly select a sample of 25 batteries in order to test the process.
(a) Describe the sampling distribution of the sample mean lifetime of batteries
(b) State a range within which you would expect the middle 90% of the sample means to lie.
(c) If the process were working correctly, what is the probability that a sample would produce a mean of less than 340 minutes?
(d) Based on your answer to part (c), what would you conclude about the process if the sample produced a mean life of batteries of 340 minutes?
(e) What is the probability that two samples in a row would have a mean life time of less than 340 minutes?