Answer to Question #311742 in Statistics and Probability for gel

Question

A manufacturer of light bulbs produces bulbs that last a mean of 950 hours with a standard deviation of 120 hours. What is the probability that the mean lifetime of a random sample of 10 of these bulbs is less than 900 hours? what is the sampling distribution of the sample means

Answer 1

$P(\bar X<900)=P(Z<\frac{900-950}{\frac{120}{\sqrt{10}}})=P(Z<-1.32)=0.0934.$

Sampling distribution: $\mu_{\bar X}=950,\sigma_{\bar X}=\frac{120}{\sqrt{10}}=37.95.$