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Sphinxa [80]
3 years ago
9

The life of light bulbs is distributed normally. The standard deviation of the lifetime is 25 hours and the mean lifetime of a b

ulb is 510 hours. Find the probability of a bulb lasting for at most 552 hours.
Mathematics
1 answer:
lesya [120]3 years ago
7 0

Answer:

<em>The  probability of a bulb lasting for at most 552 hours.</em>

<em>P(x>552)  = 0.0515</em>

Step-by-step explanation:

<u><em>Step(i):</em></u>-

Given mean of the life time of a bulb = 510 hours

Standard deviation of the lifetime of a bulb = 25 hours

Let 'X' be the random variable in normal distribution

Let 'x' = 552

Z = \frac{x-mean}{S.D} = \frac{552-510}{25} =1.628

<u><em>Step(ii):-</em></u>

<em>The  probability of a bulb lasting for at most 552 hours.</em>

<em>P(x>552) = P(Z>1.63)</em>

<em>                = 1- P( Z< 1.63)</em>

<em>                =  1 - ( 0.5 + A(1.63)</em>

<em>               =   1- 0.5 - A(1.63)</em>

<em>               =   0.5 -A(1.63)</em>

<em>               =   0.5 -0.4485</em>

<em>              =  0.0515</em>

<u><em>Conclusion:-</em></u>

<em>The  probability of a bulb lasting for at most 552 hours.</em>

<em>P(x>552)  = 0.0515</em>

<em>           </em>

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