The daily profit from a juice vending machine placed in an office building is a value of a normal random variable with unknown mean μ and variance σ2.

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 μ0 = $30.00 and standard deviation

σ0 = $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

(a) a Bayes estimate of the true average daily profit for this building;

(b) a 95% Bayesian interval of μ for this building;

(c) the probability that the average daily profit from the machine in this building is between $24.00 and

$26.00.