The life of light bulbs is distributed normally. the variance of the lifetime is 625 and the mean lifetime of a bulb is 530 hours. find the probability of a bulb lasting for at most 564 hours. round your answer to four decimal places.

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shubhamchouhanvrVT shubhamchouhanvrVT · Answer 1 · 2022-06-28T12:46:16+02:00

Using the normal distribution, it is found that there is a 0.877 = 87.7% probability of a bulb lasting for at most 569 hours.

The z-score of a measure X of a normally distributed variable with mean and standard deviation is given by:

[tex]z =\dfrac{X - \mu}{\sigma}[/tex]

The z-score measures how many standard deviations the measure is above or below the mean.
Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

[tex]\mu[/tex] = 530 [tex]\sigma^2[/tex] = 625 [tex]\sigma =[/tex] 25

The probability of a bulb lasting for at most 569 hours is the p-value of Z when X = 569, hence:

[tex]z =\dfrac{X - \mu}{\sigma}[/tex]

z = [tex]\dfrac{564 -530}{25}[/tex] = 1.36

Z = 1.36 has a p-value of 0.9131

0.9131 x 100 = 91.31 % probability of a bulb lasting for at most 569 hours.

More can be learned about the normal distribution at brainly.com/question/24663213

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