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The life of light bulbs is distributed normally. The variance of the lifetime is 900 and the mean lifetime of a bulb is 520 hours. Find the probability of a bulb lasting for at most 576 hours. Round your answer to four decimal places.

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Answer:

0.969

Step-by-step explanation:

Given that:

Mean lifetime (m) = 520 hours

Variance = 900

Hence, standard deviation (s) = √900 = 30

Probability that bulb will last for at most 576 hours

X ≤ 576

Obtain the standardized score :

Using the relation :

Zscore = (x - m) / s

Zscore = (576 - 520) / 30

Zscore = 56 / 30

Zscore = 1.867

P(Z ≤ 1.867) : using the z probability calculator ;

P(Z ≤ 1.867) = 0.96905

Hence, P(Z ≤ 1.867) = 0.969