Question 1074987: 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 910 hours, with a standard deviation of 88 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.
GIVEN
randomly selects 1000
mean 910 hours
standard deviation of 88 hours.
Find ___% Between 734 hours and 1086 .
at 36% FIND hours
empirical rule, approximately 99.7% FIND hours
empirical rule at ___ % between 734 hours and 1086
ANSWER THE FOLLOWING QUESTIONS
(a) According to Chebyshev's theorem, at least _______% of the lifetimes lie between 734 hours and 1086. Drop down choices are: 56%, 75%, 84%, 89%
(b) According to Chebyshev's theorem, at least 36% of the lifetimes lie between ___hours and ____ hours. (Round your answer to the nearest integer.)
(c) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately 99.7% of the lifetimes lie between ____ hours and ____ hours.
d) Suppose that the distribution is bell-shaped. According to the empirical rule, approximately _______% of the lifetimes lie between 734 hours and 1086 .
Drop down choices are: 68%, 75%, 95%, 99.7%
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! The first is 95%, because 734 and 1086 are -2 sd and +2 sd from mean.
Find 36% is not clear. If it means where is the middle 36%, one looks in the table at 0.32 and 0.68, which is the middle 36% and finds z=-0.47 and z=+0.47
multiply 0.47*88 to get 41.36 or 41.4
Add and subtract that to the mean to get (868.6, 951.4).
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Empirical rule for 99.7% is +/- 3 sd or +/-264
(646, 1174)
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Chebyshev's for +/-2 sd at least 3/4 (1-1/sd^2; 1-1/4) or 75%.
For the next one 36% is 1-0.64 where 0.64 is 1/x^2, where x= # sd s.
x^2=1/0.64
x=1/0.8=1.25 sd s
This is 88*1.25 or 110
(800, 1020)
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c I answered above.
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d is 95% as outlined above.
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