Question

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 857 hours, with a standard deviation of 100 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 ?56%75%84%89% of the lifetimes lie between 607 hours and 1107. (b) According to Chebyshev's theorem, at least ?56%75%84%89% of the lifetimes lie between 657 hours and 1057. (c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately ?68%75%95%99.7% of the lifetimes lie between 657 hours and 1057. (d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 68% of the lifetimes lie between hours and hours .

Answer 1

(a)

= 857

= 100

X= 607

k=(X-)/

= (607 - 857)/100

= - 2.5

X= 1107

k=(X-)/

= (1107 - 857)/100

= 2.5

= 84%

So,answer is:

According to Chebyshev's theorem, at least 84% of the lifetimes lie between 607 hours and 1107.

(b)

X= 657

k=(X-)/

= (657 - 857)/100

= - 2

X= 1057

k=(X-)/

= (1057 - 857)/100

= 2

= 75%

So,answer is:

According to Chebyshev's theorem, at least 75% of the lifetimes lie between 607 hours and 1107.

(c)

According to the empirical rule, approximately 95% of the lifetimes lie between 657 hours and 1057.

(d)

= 857 - 100 = 757

= 857 + 100 = 957

According to the empirical rule, approximately 68% of the lifetimes lie between 757 hours and 957 hours.