Question

2. The daily profit X from a drink vending machine placed in the entrance area of a school building of a university follows the normal distribution N(μ, σ2) with unknown μ and σ2. Naturally, the mean (the average daily profit) varies from building to building. Based on past experience, it is determined that μ follows a normal distribution with mean μ°-$30 and standard deviation Do $1.75. If one of these drink machines in a certain building shows an average daily profit of $24.90 during a 30-day test period with a standard sample deviation s $2.10, solve the following (a) Find the Bayesian estimate of the average daily profit for this building (b) Determine a 95% Bayesian interval for estimating μ (c) What is the probability that the average daily profit from the machine in this building is between $24.00 and $26.00? (Hint: Since σ is unknown and the sarnple size n = 30 is considered large enough, you may use s to approximate o in this problem.)

Answer 1

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