$(1$ point$)$ A random sample of $90$ observations produced a mean of $\stackrel{}{x}=35\mathrm{.}3$ from a population with a normal distribution and a standard deviation $=2\mathrm{.}66.$

$($a$)$ Find a $90\%$ confidence interval for $$

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$($b$)$ Find a $99\%$ confidence interval for $$

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$($c$)$ Find a $95\%$ confidence interval for $$

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