Answer to Question #178244 in Statistics and Probability for Roy Teodoro

Question

a manufacturer of light bulbs produces bulbs that last a mean of 950 hours with a standard deviation of 12 hours what is the probability that the mean lifetime of the random sample of 10 of these bulbs is less than 90 hours

Answer 1

$\text{let X a random variable showing the life of an incandescent lamp in hours }$

$\mu= 950;\sigma=$ 12

$X∼N(μ,σ^2/n)$

$Z= \frac{X-\mu}{\sigma/\sqrt{n}}$

$P(X<90)=P(Z<\frac{90-950}{12/\sqrt{10}})=P(Z<-226)=0$

Answer: 0 is probability that the mean lifetime of the random sample of 10 of these bulbs is less than 90 hours