The amount of pollutants that are found in waterways near large cities is normally distributed with mean 9.3 ppm and standard deviation $1.8 \mathrm{ppm} .9$ randomly selected large cities are studied. Round all answers to 4 decimal places where possible.
a. What is the distribution of
b. What is the distribution of $x$ ? $x-\mathrm{N}(9.3$
c. What is the probability that one randomly selected city's waterway will have less than $9.9 \mathrm{ppm}$ pollutants?
d. For the 9 cities, find the probability that the average amount of pollutants is less than $9.9 \mathrm{ppm}$.
e. For part d), is the assumption that the distribution is normal necessary? $\mathrm{O}$ Yes $\mathrm{No} 0^{\circ}$
f. Find the IQR for the average of 9 cities.
\[
\begin{array}{l}
\mathrm{Q} 1=\square \mathrm{ppm} \\
\mathrm{Q}=\square \mathrm{ppm} \\
\mathrm{IQR}: \square \mathrm{ppm}
\end{array}
\]
ppm $\mathrm{ppm}$
IQR: ppm

Step 1 ：The distribution of x is given as \(N(9.3, 1.8)\).

Step 2 ：The probability that one randomly selected city's waterway will have less than 9.9 ppm pollutants can be calculated using the cumulative distribution function (CDF) of the normal distribution. The probability is approximately \(0.6306\).

Step 3 ：For the 9 cities, the mean and standard deviation need to be adjusted to calculate the probability that the average amount of pollutants is less than 9.9 ppm. The adjusted mean is \(9.3\) and the adjusted standard deviation is \(0.6\). The probability is approximately \(0.8413\).

Step 4 ：The assumption that the distribution is normal is necessary for the calculations in part d. So, the answer is Yes.

Step 5 ：The interquartile range (IQR) for the average of 9 cities can be calculated using the quantile function of the normal distribution. The IQR is approximately \(0.8094\) ppm.

Step 6 ：Final Answer: \(\boxed{a. N(9.3, 1.8)}\), \(\boxed{b. N(9.3, 1.8)}\), \(\boxed{c. 0.6306}\), \(\boxed{d. 0.8413}\), \(\boxed{e. Yes}\), \(\boxed{f. 0.8094 ppm}\)