Question

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.

Answer 1

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

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