In a certain year, according to a National Census, the number of people in a household had a mean of 4.52 and a standard deviation of 2.23. This is based on census information for the population. Suppose the Census Bureau instead had estimated best main using a random sample of 375 homes. Suppose the sample had a sample mean 4.2 and a standard deviation of 2.4What is the random variable X?(a)The number of households in the country.(b) The number of people in the household. c) The number of households and the sample.(d) The mean number of people in a household. Is X quantitative or categorical?(a) The variable X is categorical, because each observation belongs to one of a set of distinct categories(b)The variable X is quantitative, because each observation belongs to one of a set of distinct values(c)The variable X is quantitative, because each observation is a numerical value of that represents and magnitude of the variable(d)The variable X is categorical, because despite the observations being numerical values the observations do not represent a magnitude of the variable Describe the center and the variability of the population distribution. What would you predict the shape of the population distribution? Explain