Young's modulus is a quantitative measure of stiffness of an elastic material. Suppose that for metal sheets of a particular type, its mean value and standard deviation are $70$GPa and $2\mathrm{.}1$GPa, respectively. Suppose the distribution is normal.

$($Round your answers to four decimal places.$)$

$($a$)$ Calculate $P(69\stackrel{}{x}71)$ when $n=25.$

$($b$)$ How likely is it that the sample mean diameter exceeds $71$ when $n=36?$

You may need to use the appropriate table in the Appendix of Tables to answer this question.

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