A local authority installs 2000 electric lamps. The life of lamps in hours (X) follows a normal distribution, where X ~ N (1000, 40,000). Calculate: 

(a) The number of lamps that might be expected to fail within the first 700 hours; 

(b) The number of lamps that may be expected to fail between 900 and 1300 hours; 

(c) After how many hours would we expect 10% of the lamps to fail? From this information we have population mean, μ, of 1000 hours with a variance, σ², of 40,000 hours2. This problem can be solved using either the NORM.DIST () or NORM.S.DIST () Excel functions as illustrated in Figure 4.13.