Answer to Question #139221 in Statistics and Probability for Airra Santiago

Question

The lifetimes of the light bulbs produced by Filip Company are normally distributed with a mean of 1,150 hours and a standard deviation of 175 hours.

What is the probability that a randomly chosen light bulb will have a life time of more than 1000 hours?
What percentage of the light bulbs would be expected to last between 1000 and 1500?

Answer 1

$\mu=1150$

$\sigma=175$

$P(X>1000) = 1-P(X<1000)=1-P(Z<\frac{1000-\mu}{\sigma})=$

$=1-P(Z<\frac{1000-1150}{175})=1-P(Z<-0.86)=1-0.1949=0.8051$

Answer: the probability that a randomly chosen light bulb will have a life time of more than 1000 hours is 0.8

$P(1000<X<1500)=P(1000<X<1500)=$

$=P(\frac{1000-\mu}{\sigma}<Z<\frac{1500-\mu}{\sigma})=$

$=P(\frac{1000-1150}{175}<Z<\frac{1500-1150}{175})=P(-0.86<Z<2)=$

$=P(Z<2)-P(Z<-0.86)=0.9772-0.1949=0.7823$

Answer:  78.23% of the light bulbs would be expected to last between 1000 and 1500