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146 JMP Means Business: Statistical Models for Management Using the light bulb life example in which individual light bulbs have a mean life of 10000 hours with a standard deviation of 1500 hours, calculate the probability that the average life of four light bulbs is less than 8500 hours. To answer this question, note that n = 4, µ = 10000, and = 1500. The probability that the average life of four light bulbs is less than or equal to 8500 hours is 8500 - 10000 P [ Y 8500 ] = P Z = P [ Z - 2 ] = . 02275 1500 4 This probability is smaller than the probability that the life of an individual light bulb is less than or equal to 8500 hours with Z = [8500 10000]/1500 = 1 and P[Y 8500] = P[Z 1] =.15866. In addition to the uniform and Normal distributions, there are several other continuous distributions that find frequent use in business applications: Exponential: The exponential distribution is continuous with non-negative outcome values. The exponential distribution is important in the fields of reliability, survival studies, telecommunications, and modeling queuing behavior. It models phenomena with constant failure rates. Lognormal: The lognormal distribution is continuous with non-negative outcome values. The lognormal distribution serves as a conceptual model in a wide variety of disciplines, including product life, economics, biology, pharmaceuticals, and materials science. It is often appropriate for outcomes that span orders of magnitude (powers of 10).