According to the U.S. Census Bureau, the number of people in a household has a mean of 2.6 and a standard deviation of 1.5. Suppose the Census Bureau instead had estimated this mean using a random sample of 225 homes, and that sample had a mean of 2.4 and standard deviation of 1.4.

For the sampling distribution:

(a) specify its mean and its standard deviation (standard error).

(b) specify its shape.

(c) Sketch the sampling distribution of the sample mean for n = 225.

(d) Describe the center and spread of the sample data distribution.