AP Stat Worksheet

AP Stat WorksheetName______Per___

CRACKER JACKS PROBLEM

Suppose there are 5 prizes in boxes of Cracker Jacks: A Whistle, a Ring, a Key Chain, a Ball, and a Puzzle. Because you like solving puzzles so much, you have decided to continue buying (and eating) Cracker Jacks until you get your puzzle prize.

a) Simulate this problem 20 times keeping track of the number of boxes you must buy before getting your favorite puzzle prize. Enter Line 101 on your Table of Random Digits. Be sure to describe how you will go about your simulation so that someone can follow what you did.

b) Describe the shape of your frequency distribution.

c) Estimate (from your simulation) the percent chance of getting the puzzle on the 1st trial. How about the 2nd trial? How about the 15th trial?

1st:2nd: 15th:

Now let's look at this problem from a theoretical standpoint.

d) Place #'s1-20 into L1 and the corresponding theoretical probabilities of getting the puzzle on the xth trial into L2. Does Scatter Plot(L1 , L2) look anything like your simulated frequency table? Sketch it below.

e) Suppose now there are 5000 children (you are one of them) who all want the puzzle. Suppose each child keeps buying Cracker Jacks until he/she gets the puzzle. Using your probabilities in L2, place the number of children (out of 5000) getting the puzzle on the xth trial into L3. What percent of the children got the puzzle on their 1st trial? How many children got the puzzle on their 1st trial? What percent of the children got the puzzle on their 2nd trial? How many children got the puzzle on their 2nd box of Cracker Jacks? What percent of the children got the puzzle on their 15th trial? How many children got the puzzle on their 15th box of Cracker Jacks?

PercentNumber of Children

1st trial:

2nd trial:

15th trial:

f) What is the theoretical probability of having to buy 6 or fewer boxes?

g) What is the theoretical probability of having to buy 8 or more boxes?

h) Build Scatter Plot (L1 , L3). Does this scatter plot of the number of children vs. the number of boxes look anything like your Scatter

Plot(L1 , L2)?

i) Write the equation of the curve that will contain all of your points on your Scatter Plot(L1 , L2).

j) By taking the square root or logarithm of L2(choose the right one), build a scatter plot of this linear data. Now do the same to your equation in (i) and write the equation of this linear relationship in y=a+bx form. List the values of both ab.

a=b=

AP Stat Worksheet Name______Per___

Shaq’s Free Throw Problem

Suppose Shaquille O’Neal is shooting free throws with a success rate of about 30%. Simulate the number of free throws that Shaq will sink in 5 tries. Enter Line 148 of your Random Digit Table and perform 24 simulations. Show a frequency table along with both the estimated and theoretical probabilities below.

1) Describe this frequency distribution.

(2-7) Give both the a) estimated and b) theoretical answers to each.

a) b)

2) P(x=2)=

3) P(x2)=

4) P(x2)=

5) P(x=0)=

6) P(x1)=

7) Find both the estimated and the theoreticalmean and standarddeviation.

Shaq’s Other Free Throw Problem

Now suppose Shaq keeps shooting free throws until he makes one. Once he sinks a free throw, he feels he has put in a day’s work and takes himself out of the game! Simulate 40 games for Shaq. Enter Line 136. a) Est b) Theo

# Free Throws freq Est. Prob. Theo. Prob. Cumm. Prob. 1) P(x=2)

before make

X 2) P(x3)

1 3) P(x4)