- Question 3 25 Marks Battery Manufacturers Claim That Their Batteries Have A Mean Life Of 50 Months With A Standard Dev 1 (110.95 KiB) Viewed 27 times
Question 3 [25 marks] Battery manufacturers claim that their batteries have a mean life of 50 months with a standard deviation of 6 months. Suppose the distribution of battery lives of this brand is approximately normal. (a) On the assumption that the manufacturer's claims are true, find the probability that a randomly selected battery of this type will last less than 48months. [5 marks] (b) On the same assumption, find the probability that the mean of a random Sample of 25 such batteries will be less than 48 months. [5 marks] (c) On the same assumption, find the probability that the mean of a random Sample of 36 such batteries will be less than 48 months. [5 marks] (d) On the same assumption, find the probability that the mean of a random Sample of 49 such batteries will be less than 48 months [5 marks] (e) Using your findings in (a)-(d), comment on the relationship between population distribution and sampling distributions. [5 marks]