In: Statistics and Probability
BIG Corporation produces just about everything but is currently interested in the lifetimes of its batteries, hoping to obtain its share of a market boosted by the popularity of portable CD and MP3 players. To investigate its new line of Ultra batteries, BIG randomly selects 1000 Ultra batteries and finds that they have a mean lifetime of 927 hours, with a standard deviation of 83 hours. Suppose that this mean and standard deviation apply to the population of all Ultra batteries. Complete the following statements about the distribution of lifetimes of all Ultra batteries.
(a) According to Chebyshev's theorem, at least ______ of the lifetimes lie between 678 hours and 1176 hours.
(b) According to Chebyshev's theorem, at least ______ of the lifetimes lie between 761 hours and 1093 hours.
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately ________ of the lifetimes lie between 761 hours and 1093 hours.
(d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the lifetimes lie between ______ hours and ______ hours.