A confidence interval for a population mean is to be estimated. The population standard deviation is guessed to be anywhere from 14 to 24. The half-width B desired could be anywhere from 2 to 7.

a. Tabulate the minimum sample size needed for the given ranges of the population standard deviation and B.

b. If the fixed cost of sampling is $350 and the variable cost is $4 per sample, tabulate the sampling cost for the given ranges of the population standard deviation and B.

c. If the cost of estimation error is given by the formula 10 B² tabulate the total cost for the given ranges of population standard deviation and B. What is the value of B that minimizes the total cost when the population standard deviation = 14? What is the value of B that minimizes the total cost when population standard deviation = 24?