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# Probability : Bayesian Statistics

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Bayesian Statistics

The daily profit from a juice vending machine placed in an office building is a value of a normal random variable with unknown mean Î¼ and variance Ïƒ2. Of course, the mean will vary somewhat from building to building, and the distributor feels that these average daily profits can best be described by a normal distribution with mean Î¼0 = \$30.00 and standard deviationÏƒ0 = \$1.75. If one of these juice machines, placed in a certain building, showed an average daily profit of x = \$24.90 during the first 30 days with a standard deviation of s = \$2.10, find

(b) a 95% Bayesian interval of Î¼ for this building;
(c) the probability that the average daily profit from the machine in this building is between \$24.00 and \$26.00.