Distinguish between one-tailed and two-tailed tests.

Solve the following linear programming problem:

Min

Distinguish between the characteristics of first and second order difference equations. Give examples of economic problems that are solved with the help of each category of such equations.

What is p- value?

What is the probability that neither will be red?

What is the probability that the first ball will be red and the second yellow?

(a) What is the normal probability distribution function? State its properties.

(b) The concentration of impurities in a semiconductor used in the production of microprocessors for computer is a normally distributed random variable with mean 127 parts per million and standard deviation 22. A semiconductor is acceptable only if its concentration of impurities is below 150 parts per million. What proportions of the semiconductors are acceptable for use? (The area under the standard normal curve for the value of z = 1.5 is 0.668).