The mean lifetime of a bulb is 520 hours, while the variance of the lifetime is 225. The probability that a light bulb will survive at most 533 hours is 0.86.
Given that,
The lifespan of light bulbs is generally distributed. The mean lifetime of a bulb is 520 hours, while the variance of the lifetime is 225.
We have to calculate the probability that a light bulb will survive at most 533 hours.
We would use the normal distribution formula, which is stated as, because the lifespan of light bulbs is distributed regularly,
z = (x - µ)/σ
Where
x = life of light bulbs.
µ = mean lifetime
σ = standard deviation
From the information given,
µ = 520 hours
Variance = 225
σ = √variance = √225
σ = 15
The probability that a light bulb will last for no more than 560 hours is given by
P(x ≤ 533)
For x = 533
z = (533 - 520)/15 = 0.86
According to the normal distribution table, 0.86 represents the probability for the z score.
Therefore, the probability that a light bulb will survive at most 533 hours is 0.86.
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