Alumber company is making boards that are 2697.0 millimeters tall. if the boards are too long they must be trimmed, and if they are too short they cannot be used. a sample of 25 boards is made, and it is found that they have a mean of 2697.4 millimeters with a standard deviation of 10.0 . is there evidence at the 0.1 level that the boards are either too long or too short? assume the population distribution is approximately normal.

a. determine the decision rule for rejecting the null hypothesis.
b. make the decision to reject or fail to reject the null hypothesis.

Acar dealership pays you 5% commission on your first $10,000 on car sales and 8% commission on the sale amount over $10,000 if you sold a $12,000 car how much is your commission

What is the slope of the line that contains the points (4,8) and (9,8)? what type of line is it?

Asays "we are both knaves" and b says nothing. exercises 24–31 relate to inhabitants of an island on which there are three kinds of people: knights who always tell the truth, knaves who always lie, and spies (called normals by smullyan [sm78]) who can either lie or tell the truth. you encounter three people, a, b, and c. you know one of these people is a knight, one is a knave, and one is a spy. each of the three people knows the type of person each of other two is. for each of these situations, if possible, determine whether there is a unique solution and determine who the knave, knight, and spy are. when there is no unique solution, list all possible solutions or state that there are no solutions. 24. a says "c is the knave," b says, "a is the knight," and c says "i am the spy."