Question

The lifetimes of light bulbs are normally distributed with a mean of 500 hours and a standard deviation of 25 hours. Find the probability that a randomly selected light bulb has a lifetime that is greater than 532 hours.

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Answer 1

Given Mean of light bulbs, = 500

Standard Deviation = 25 hours

Probability that a randomly selected light bulb has a lifetime that is greater than 532 hours is P(X > 532)

Here the random variable X is the number of hours of lifetime of the bulb

Given that the lifetimes of light bulbs are normally distributed

We need to find P(X > 532)

z-score = (X - ) /

= (532 - 500) / 25

= 32 / 25

= 1.28

The area to left of z-score 1.28 will give us P(X < 532)

P(X < 532) which is the area to the left of z-score =  0.89973 from the below attached z-table

P(X < 523) + P(X > 532) = 1

0.89973 + P(X > 532) = 1

P(X > 532) = 1 - 0.89973

= 0.10027

So Probability that a randomly selected light bulb has a lifetime that is greater than 532 hours is 0.10027