As a result of tests on 20,000 bulbs manufactured by a company , it was found that life times of bulbs were normally distributed with an average life of 2040 hours and standard deviation of 60 hours.
(i) Estimate the number of bulbs whose lifetime is more than 1960 hours; and
(ii) Find the minimum lifetime of the best 2500 bulbs.
Answers
Given : 20,000 bulbs manufactured by a company , it was found that life times of bulbs were normally distributed with an average life of 2040 hours and standard deviation of 60 hours.
To Find :
(i) Estimate the number of bulbs whose lifetime is more than 1960 hours; and
(ii) Find the minimum lifetime of the best 2500 bulbs.
Solution:
Mean = 2040 hrs
SD = 60 hrs
Z score = ( Value - Mean) /SD
lifetime is more than 1960 hours
= ( 1960 - 2040)/60
= -80/60
= - 1.333
= 9.1%
of 20000 = 1820
20000 - 1820 = 18180 bulbs life time more than 1960 hours
minimum lifetime of the best 2500 bulbs.
(20000 - 2500) = 17500
= (17500/20000) * 100 = 87.5 %
Z score = 1.15
1.15 = ( value - 2040)/60
=> 69= value - 2040
=> Value = 2109
2109 hrs is minimum lifetime of the best 2500 bulbs.
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