1 answer

Light bulbs are found to have a mean life of 800 hours. The standard deviation is...

Question:

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


Answers

Solution :

Given that,

mean = \mu = 800

standard deviation = \sigma = 160

n = 400

\mu\bar x =800

\sigma\bar x = \sigma / \sqrt n = 160 \sqrt 400 = 8

P (798 < x < 802 )

P ( 798 - 800 / 8) < ( \bar x - \mu \bar x /\sigma\bar x) < ( 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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