Please answer the following question and show work! Answer all parts. Thank you **7.81 Household Size**In Example 7.9 on page 322, we conducted a simulation to check the plausibility of the central limit theorem. The variable under consideration is household size, and the population consists of all U.S. households. A frequency distribution for household size of U.S. households is presented in Table 7.7.a. Suppose that you simulate 1000 samples of four households each, determine the sample mean of each of the 1000 samples, and obtain a histogram of the 1000 sample means. Would you expect the histogram to be bell-shaped? Explain your answer.b. Carry out the tasks in part (a) and note the shape of the histogram.c. Repeat parts (a) and (b) for samples of size 10.d. Repeat parts (a) and (b) for samples of size 100. **Table 7.7: Frequency Distribution for U.S. Household Size**This table represents the frequency distribution of different household sizes in the United States, measured in millions. It is structured into two columns:- **Number of People**: This column lists the possible number of people in a household, ranging from 1 to 7. - **Frequency (millions)**: This column shows how many millions of households there are for each corresponding household size.Here is the data distribution:- Households with 1 person: 31.4 million- Households with 2 people: 39.5 million- Households with 3 people: 18.6 million- Households with 4 people: 16.1 million- Households with 5 people: 7.4 million- Households with 6 people: 2.8 million- Households with 7 people: 1.7 millionThe table provides insight into the prevalence of various household sizes across the U.S., highlighting that 2-person households are the most common, followed by 1-person households.

Given that - A simulation to check the plausibility of the central limit theorem. The variable under consideration there is household size, and the population consists of all U.S. households. A frequency distribution for household size of U.S. households is presented in Table. Number of people Frequency 1 31.4 2 39.5 3 18.6 4 16.1 5 7.4 6 2.8 7 1.7a) A histogram of the 1000 sample means will be bell shaped.Sample sizes equal to or greater than 30 are often considered sufficient for the central limit theorm to hold.b) bell shaped histogramc) sample size n = 10here n ≤ 30 so does not meet the criteria of central limit theormso, histogram look like a skewed.d) sample size n = 100here n > 30 are often considered sufficient for the central limit theorm to hold. the histogram look like a bell shaped.