Light bulbs are found to have a mean life of 800 hours. The standard deviation is 160. A sample of 400 is chosen. Find the probability that 798 < x < 802
Solution :
Given that,
mean = = 800
standard deviation = = 160
n = 400
=800
= / n = 160 400 = 8
P (798 < x < 802 )
P ( 798 - 800 / 8) < ( - /) < ( 802 - 800 / 8)
P (- 2 / 8< z < 2 / 8 )
P (-0.25 < z < 0.25 )
P ( z < 0.25 ) - P ( z < -0.25)
Using z table
= 0.5987 - 0.4013
= 0.1974
Probability = 0.1974
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