Introduction to Statistics / MAT300 SPRING 2014

1.Chebyshev’s theorem and the empirical rule

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 Ultra batteries and finds that they have a mean lifetime of hours. Suppose that this mean applies to the population of all Ultra batteries. Complete the following statements about the distribution

of lifetimes of all Ultra batteries.

(a) According to Chebys hev’s theorem , at least ? of the lifetim es lie within 1.5 s tandard deviations of the m ean, 890 hours .

(b) Suppos e that the dis tribution is bell-s haped. If approxim ately 68% of the lifetim es lie between 795 hours and 985 hours , then the approxim ate value of the s tandard deviation for the dis tribution, according to the em pirical rule, is .