According to the U.S. Census Bureau, the distribution of family sizes in the United States for...

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According to the U.S. Census Bureau, the distribution of family sizes in the United States for the year 2000 is as shown ins the following table. (The term "family" refers to a group of two or more people related by birth, marriage, or adoption and residing together in a household. The term "household" refers to all people who occupy a "housing unit," that is, a house, an apartment, or other group of rooms, or a single room that constitutes "separate living quarters.") Size of family (for 2000) 2 Number of families Percentage of families (in thousands) 31,455 44.3 3 16,073 22.9 4 14,496 20.0 5 6,526 08.6 6 2,226 02.8 7* 1,249 01.4 *This category is actually "7 or more," but very few families have more than 7 members. That is, 44.3% of the families in the United States have two members, whereas only 2.8% have six members. (Families with more than seven children are very rare.) (a) Find the mean family size, approximately, from this distribution of family sizes. Will this approximation be too large or too small? Explain. (b) Find the approximate standard deviation of the family sizes. (c) Suppose Nielsen randomly selects 400 families from this population. Describe, as closely as you can, the shape, center, and spread of the 400 data values that might occur in the sample. (d) Nielsen is actually interested in the mean number of persons per family in samples of 400 families. Describe, as closely as you can, the shape, center, and spread of the distribution of possible values of the sample mean in random samples of 400 families. According to the U.S. Census Bureau, the distribution of family sizes in the United States for the year 2000 is as shown ins the following table. (The term "family" refers to a group of two or more people related by birth, marriage, or adoption and residing together in a household. The term "household" refers to all people who occupy a "housing unit," that is, a house, an apartment, or other group of rooms, or a single room that constitutes "separate living quarters.") Size of family (for 2000) 2 Number of families Percentage of families (in thousands) 31,455 44.3 3 16,073 22.9 4 14,496 20.0 5 6,526 08.6 6 2,226 02.8 7* 1,249 01.4 *This category is actually "7 or more," but very few families have more than 7 members. That is, 44.3% of the families in the United States have two members, whereas only 2.8% have six members. (Families with more than seven children are very rare.) (a) Find the mean family size, approximately, from this distribution of family sizes. Will this approximation be too large or too small? Explain. (b) Find the approximate standard deviation of the family sizes. (c) Suppose Nielsen randomly selects 400 families from this population. Describe, as closely as you can, the shape, center, and spread of the 400 data values that might occur in the sample. (d) Nielsen is actually interested in the mean number of persons per family in samples of 400 families. Describe, as closely as you can, the shape, center, and spread of the distribution of possible values of the sample mean in random samples of 400 families.