Question

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.

Answer 1

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.

What is Normal Probability Distribution?

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

$z =\dfrac{X - \mu}{\sigma}$

• 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:

$\mu$ = 530  $\sigma^2$ = 625 $\sigma =$ 25

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

$z =\dfrac{X - \mu}{\sigma}$

z = $\dfrac{564 -530}{25}$ = 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

#SPJ1