Inferential Statistics - Normal Distribution

Question

The city government conducted a new street lighting project by installing 2500 electric lamps. According to them, the lamps are made by different manufacturing company and have a 1050 hours average burn time. Based on their previous experience, the distribution of the burning lives is close to normal. During their observation, they found out the 250th light bulbs burned out after 819 hours. For this group of lamps, what is the standard deviation of their burning lives?

Answer 1

250/2500 = .1

For z ~ N(0,1) , if P(Z ,= z) = .1, z = phi^-1(.1) = , from Excel, normsinv(.1) = -1.28155

As z = (819 - 1050)/sigma, sigma = (819-1050)/z = (819-1050)/ -1.28155 = 180.2503