In a certainyear, according to a national CensusBureau, the number of people in a household had a mean of4.55 and a standard deviation of2.91. This is based on census information for the population. Suppose the Census Bureau instead had estimated this mean using a random sample of225homes. Suppose the sample had a sample mean of4.8 and standard deviation of3.2. Complete parts a through d below.

a. Identify the random variable X. Indicate whether it is quantitative or categorical.

What is the random variableX?

1. The number of households in the sample
2. The mean number of people in a household
3. The number of people in a household
4. The number of households in the country

Is X quantitative orcategorical?

b. Describe the center and variability of the population distribution. What would you predict as the shape of the populationdistribution? Explain.

The center of the population distribution is _____

(Round to two decimal places asneeded.)

The variability of the population distribution is _____

(Round to two decimal places asneeded.)

c. Describe the center and variability of the data distribution. What would you predict as the shape of the datadistribution? Explain.

The center of the data distribution is _____

(Round to two decimal places asneeded.)

The variability of the data distribution is_____

(Round to two decimal places asneeded.)

d. Describe the center and variability of the sampling distribution of the sample mean for

350 homes. What would you predict as the shape of the samplingdistribution? Explain.

The center of the sampling distribution of the sample mean is_____

(Round to two decimal places asneeded.)

The variability of the sampling distribution of the sample mean is_____

(Round to two decimal places asneeded.)