1.Three-circle, red-on-white is one distinctive pattern painted on ceramic vessels of the Anasazi period found at the Wi

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1.Three-circle, red-on-white is one distinctive pattern paintedon ceramic vessels of the Anasazi period found at the Wind Mountainarchaeological site. At one excavation, a sample of 174 potsherdsindicated that 80 were of the three-circle, red-on-white pattern.How many ceramic potsherds must be found and identified if we areto be 95% confident that the sample proportion p̂ of such potsherdsis within 6.0% of the population proportion of three-circle,red-on-white patterns found at this excavation site? (Round youranswer up to the nearest whole number.)
2. Three-circle, red-on-white is one distinctive pattern paintedon ceramic vessels of the Anasazi period found at an archaeologicalsite. At one excavation, a sample of 173 potsherds indicated that80 were of the three-circle, red-on-white pattern. (a) Find a pointestimate p̂ for the proportion of all ceramic potsherds at thissite that are of the three-circle, red-on-white pattern. (Roundyour answer to four decimal places.) (b) Compute a 95% confidenceinterval for the population proportion p of all ceramic potsherdswith this distinctive pattern found at the site. (Round youranswers to three decimal places.)
3. Anystate Auto Insurance Company took a random sample of 384insurance claims paid out during a 1-year period. The average claimpaid was $1600. Assume 𝜎 = $246. Find a 0.90 confidence intervalfor the mean claim payment. (Round your answers to two decimalplaces.) Find a 0.99 confidence interval for the mean claimpayment. (Round your answers to two decimal places.)