Answer to Question #171382 in Statistics and Probability for Nana

Question

1. 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 lifetime of more than 1,000 hours?
• What percentage of the light bulbs would be expected to last between 1,000 and 1,500 hours?

Answer 1

What is the probability that a randomly chosen light bulb will have a lifetime of more than 1,000 hours?

$μ = 1150 \; hours \\ σ = 175 \;hours \\ P(X > 1000) = 1 -P(X<1000) \\ = 1 -P(Z< \frac{1000-1150}{175} \\ = 1 -P(Z<-0.8571) \\ = 1 -0.1957 \\ = 0.8043$

What percentage of the light bulbs would be expected to last between 1,000 and 1,500 hours?

$P(1000<X < 1500) = P(\frac{1000-1150}{175}<Z< \frac{1500-1150}{175}) \\ = P(-0.8571<Z<2) \\ = P(Z<2) -P(Z<-0.8571) \\ = 0.9772 -0.1957 \\ = 0.7815 \\ = 78.15 \%$