A company which manufactures and sells small electronic devices includes a small dry cell battery with each device. Because of the large quantity of batteries required it buys them in bulk. It is considering buying from a new supplier and is concerned that although the price is low the batteries may be inferior. They have purchased a trial batch of 500 batteries and have tested a random sample of 10 of them for capacity. The results in milliamp-hours are as follows. 610 480 300 520 420 680 520 450 420 650 (1) On the basis if the sample, what is the mean value of the whole batch? (i) What range of capacities would include 95% of the whole batch? (iii) What are the 95% confidence limits for the estimate of the mean value? (iv) How many would need to be sampled to determine the mean capacity within plus or minus 10 milliamp hours with a 95% confidence limit