Answer to Question #167665 in Statistics and Probability for kienth bryan doroin

Question

"An electrical firm manufactures light bulbs that have a length of life that is normally distributed with mean equal to 778 hours and a standard deviation of 43 hours. Find the probability that a bulb burns between 755 and 892 hours. 

Answer 1

We have that

$\mu = 778$

$\sigma = 43$

$P(755<X<892) =P(\frac{755-\mu}{\sigma}<Z<\frac{892-\mu}{\sigma})=P(\frac{755-778}{43}<Z<\frac{892-778}{43})=$

$=P(-0.53<Z<2.65)=P(Z<2.65)-P(Z<-0.53)=$

$=0.9960-0.2981=0.6979$

Answer: 0.6979