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Science News Online reported on tests for PFOA exposure conducted on a sample of 326 people who live near DuPont鈥檚 Teflon-making Washington. So, sample size n=326. Also, it is given that$渭=6$ and$蟽=10$

Let X be the blood concentration of PFOA.

From the given problem$渭=6$ ,$蟽=10$ and sample size is $n=326$.

According to Central limit theorem, if the sample size is large, then the sampling distribution of the sample mean $\left(\stackrel{炉}{x}\right)$becomes approximately normal.

Let,

$\begin{array}{rcl}P\left(\stackrel{炉}{x}>7.5\right)& =& P\left(\frac{\stackrel{炉}{x}-渭}{蟽}>\frac{7.5-6}{10}\right)\\ & =& P\left(Z>\frac{1.5}{0.5538}\right)\\ & =& P\left(Z>2.71\right)\\ & =& 1-P\left(Z猢�2.71\right)\\ & =& 1-\left\{0.5+P\left(0<Z<2.71\right)\right\}\\ & =& 1-0.5-0.4966\\ & =& 0.0034\\ & & \end{array}$

Thus, the probability that the average blood concentration of PFOA in the sample is greater than 7.5 ppb is 0.0034.

Now,

$\begin{array}{rcl}P\left(\stackrel{炉}{x}猢�300\right)& =& P\left(\frac{\stackrel{炉}{x}-渭}{蟽}>\frac{300-6}{10}\right)\\ & =& P\left(Z>\frac{294}{0.5538}\right)\\ & =& P\left(Z>530.88\right)\\ & =& 1-P\left(Z<530.88\right)\\ & =& 1-\left\{0.5+P\left(0<Z<530.88\right)\right\}\\ & 鈮�& 1-0.5-0.5\\ & 鈮�& 0\\ & & \end{array}$

Thus,$P\left(\stackrel{炉}{x}猢�300\right)鈮�0$

Thus, it can be concluded that the true mean$渭$ PFOA concentration for the population of people who live near DuPont鈥檚 Teflon facility is not 6 ppb but it is greater than 6ppb because the is$P\left(\stackrel{炉}{x}猢�300\right)$ absolutely zero when the population mean is 6 ppb.