1.
"margin\\ of\\ error={1 \\over 2}\\times(1536.36-1263.64)"
"margin\\ of\\ error=136.36"
2.Based on the information provided, the significance level is "\\alpha=0.01" ("99\\%" confidence interval), and the critical value for a two-tailed test is "z_c=2.58"
Given that "\\sigma=8, margin\\ of\\ error\\leq2." Then
"n\\geq({2.58\\times8 \\over 2})^2"
"n\\geq106.5"
Since "n" is integer, then "n\\geq107."
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