3. Suppose that a carton of one dozen eggs does happen to have exactly three eggs that carry salmonella and that the manager does as he proposes: selects three eggs at random and throws them out, then uses the remaining nine eggs in four-egg quiches. Let x 5 number of eggs that carry salmonella among four eggs selected at random from the remaining nine.

Working with a partner, conduct a simulation to approximate the distribution of x by carrying out the following sequence of steps:

a. Take 12 identical slips of paper and write “Good”

on nine of them and “Bad” on the remaining three. Place the slips of paper in a paper bag or some other container.

b. Mix the slips and then select three at random and remove them from the bag.

c. Mix the remaining slips and select four “eggs”

from the bags.

d. Note the number of bad eggs among the four selected. (This is an observed x value.)

e. Replace all slips, so that the bag now contains all 12 “eggs.”

f. Repeat Steps (b)–

(d) at least 10 times, each time recording the observed x value.