Suppose $p(x)$ is a polynomial of smallest possible degree such that: $\bullet$ $p(x)$ has rational coefficients $\bullet$ $p(-3) = p(\sqrt 7) = p(1-\sqrt 6) = 0$ $\bullet$ $p(-1) = 8$ determine the value of $p(0)$.

Use the given degree of confidence and sample data to construct a confidence interval for the population mean mu . assume that the population has a normal distribution. a laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 185 milligrams with sequals 17.6 milligrams. a confidence interval of 173.8 mgless than muless than 196.2 mg is constructed for the true mean cholesterol content of all such eggs. it was assumed that the population has a normal distribution. what confidence level does this interval represent?