4. One hundred draws are made at random with replacement formthe box [1  3 3  9]

Assume SD_b=3 .

a) How large can the sum be? How small?

b) Find the expected value and the standard error for the sum ofdraws.

Show them on the normal curve.

b) How likely is the sum to be in the range 370 to 430

c) How likely is the sum to be larger than 500?

6. A quiz has 25  multiple choicequestions. Each question has 3 possible answers, one of which iscorrect.  A correct answer is worth 4 points (a ticketwith the value of 4), but a point is taken off for each incorrectanswer (a ticket with the value of -1). A student answers all 25questions by guessing at random.

a) Present the problem with an appropriate box model.

Find the expected value and the standard error for the sum of 25draws. Interpret this sum in terms of the scores.

b) What is the chance that the student will get a score above50?

II:  Now replace the tickets with thevalue of -1 by the tickets with the value of 0.

a) Make a box model.  Find the expected value and thestandard error for the sum of 25 draws. Interpret the result.

b) What is the chance that the student will get a score above50?

3.  A box contains two red balls and three greenballs.

Make a box model.

Six draws are made with replacementfrom the box. Find the chancethat:

a)   A redball is neverdrawn.

b)  A green ball appears exactly three times.