The graph below displays the relative frequency distribution for X, the total number of dogs and cats owned per household, for the households in a large suburban area. For instance, 14 percent of the households own 2 of these pets.

Number of dog/ Relative Frequency
0- 0.36
1- 0.24
2- 0.14
3-0.09
4- 0.07
5- 0.04
6-0.04
7- 0.02

(a) According to a local law, each household in this area is prohibited from owning more than 2 of these pets. If a household in this area is selected at
random, what is the probability that the selected household will be in violation of this law? Show your work.

(b) If 12 households in this area are selected at random, what is the probability that exactly 3 of them will be in violation of this law? Show your
work.

(c) The mean and standard deviation of X are 1.65 and 1.851, respectively. Suppose 100 households in this area are to be selected at random and X , the
mean number of dogs and cats per household, is to be computed. Describe the sampling distribution of X , including its shape, center, and spread.