The daily profit, from a juice vending machine placed in an office building is a value of

Question:

The daily profit, from a juice vending machine placed in an office building is a value of a normal random variable with unknown mean p and variance e r n. 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 with mean μ0 = $30.00 and standard deviation σ0 = S1.75. If one of these juice machines, placed in a certain building, showed an average daily profit 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 p for this building;
(c) The probability that the average daily profit from the machine in this building is between $24.00 and $26.00.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...