The life of light bulbs is distributed normally. The standard deviation of the lifetime is 25 hours and the mean lifetime of a bulb is 510 hours. Find the probability of a bulb lasting for at most 552 hours. Round your answer to four decimal places.

Question

Mathematics

Isabela Santiago

5 June, 13:10

The life of light bulbs is distributed normally. The standard deviation of the lifetime is 25 hours and the mean lifetime of a bulb is 510 hours. Find the probability of a bulb lasting for at most 552 hours. Round your answer to four decimal places.

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Answers (1)

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Jayda Byrd · Answer 1

Answer: the probability of a bulb lasting for at most 552 hours is 0.953.

Step-by-step explanation:

Since the life of light bulbs are distributed normally, we would apply the formula for normal distribution which is expressed as

z = (x - µ) / σ

Where

x = the life of light bulbs in hours.

µ = mean hour

σ = standard deviation

From the information given,

µ = 510 hours

σ = 25 hours

We want to find the probability of a bulb lasting for at most 552 hours. It is expressed as

P (x ≤ 552)

For x = 552

z = (552 - 510) / 25 = 1.68

Looking at the normal distribution table, the probability corresponding to the z score is 0.953